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		<loc>https://www.clinicalbiostats.com/tutorials/horizontal-shells-about-a-shifted-axis/</loc>
		<lastmod>2026-10-17T23:25:51+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shell-heights-between-two-curves/</loc>
		<lastmod>2026-10-17T23:25:52+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/horizontal-shells-from-curves-written-as-x-g-y/</loc>
		<lastmod>2026-10-17T23:25:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/finding-shell-bounds-from-intersections/</loc>
		<lastmod>2026-10-17T23:25:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/piecewise-shell-setups-for-changing-boundaries/</loc>
		<lastmod>2026-10-17T23:25:54+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shells-from-regions-with-multiple-vertical-components/</loc>
		<lastmod>2026-10-17T23:25:54+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shells-from-regions-with-multiple-horizontal-components/</loc>
		<lastmod>2026-10-17T23:25:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/avoiding-double-counting-when-the-axis-crosses-the-region/</loc>
		<lastmod>2026-10-17T23:25:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shell-heights-for-regions-with-holes/</loc>
		<lastmod>2026-10-17T23:25:56+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shells-for-a-region-under-a-power-function/</loc>
		<lastmod>2026-10-17T23:25:56+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shells-for-a-line-parabola-region/</loc>
		<lastmod>2026-10-17T23:25:57+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/horizontal-shells-for-a-region-bounded-in-y/</loc>
		<lastmod>2026-10-17T23:25:58+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shells-around-an-axis-through-a-bounded-region/</loc>
		<lastmod>2026-10-17T23:25:58+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shells-versus-washers-for-the-same-solid/</loc>
		<lastmod>2026-10-17T23:25:58+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-slice-orientation-for-a-shell-integral/</loc>
		<lastmod>2026-10-17T23:25:59+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/diagnosing-radius-height-and-differential-errors/</loc>
		<lastmod>2026-10-17T23:25:59+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-piecewise-region-shell-setup-workshop/</loc>
		<lastmod>2026-10-17T23:26:00+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-shifted-axis-shell-computation-workshop/</loc>
		<lastmod>2026-10-17T23:26:00+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-complete-shell-method-volume-workshop/</loc>
		<lastmod>2026-10-17T23:26:01+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/arc-length-as-a-limit-of-chord-sums/</loc>
		<lastmod>2026-10-17T23:26:02+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-arc-length-formula-for-graphs/</loc>
		<lastmod>2026-10-17T23:26:03+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/setting-up-length-integrals-in-either-graph-orientation/</loc>
		<lastmod>2026-10-17T23:26:03+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/simplifying-graph-length-integrands/</loc>
		<lastmod>2026-10-17T23:26:04+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/substitution-patterns-for-exact-graph-lengths/</loc>
		<lastmod>2026-10-17T23:26:04+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/arc-length-of-quadratic-graphs/</loc>
		<lastmod>2026-10-17T23:26:05+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/exponential-and-logarithmic-graph-length-examples/</loc>
		<lastmod>2026-10-17T23:26:05+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/trigonometric-graphs-with-simplifiable-length-integrands/</loc>
		<lastmod>2026-10-17T23:26:06+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/finite-length-near-vertical-tangents/</loc>
		<lastmod>2026-10-17T23:26:06+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-arc-length-for-parametric-curves/</loc>
		<lastmod>2026-10-17T23:26:07+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/reparameterization-invariance-of-curve-length/</loc>
		<lastmod>2026-10-17T23:26:07+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/regularity-cusps-and-zero-speed-parameters/</loc>
		<lastmod>2026-10-17T23:26:08+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-parameters-to-simplify-curve-length/</loc>
		<lastmod>2026-10-17T23:26:08+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/arc-length-of-polynomial-parametric-curves/</loc>
		<lastmod>2026-10-17T23:26:09+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-cycloid-arch-length-calculation/</loc>
		<lastmod>2026-10-17T23:26:09+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/ellipse-circumference-and-elliptic-integrals/</loc>
		<lastmod>2026-10-17T23:26:10+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/additivity-for-piecewise-smooth-curves/</loc>
		<lastmod>2026-10-17T23:26:10+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-bounds-for-arc-length/</loc>
		<lastmod>2026-10-17T23:26:11+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/common-setup-errors-in-arc-length-problems/</loc>
		<lastmod>2026-10-17T23:26:11+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/numerical-approximation-of-arc-length-integrals/</loc>
		<lastmod>2026-10-17T23:26:12+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/simpson-s-rule-for-arc-length/</loc>
		<lastmod>2026-10-17T23:26:13+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/error-control-and-refinement-for-arc-length-estimates/</loc>
		<lastmod>2026-10-17T23:26:13+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/using-symmetry-to-reduce-arc-length-calculations/</loc>
		<lastmod>2026-10-17T23:26:14+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/comparing-graph-and-parametric-length-setups/</loc>
		<lastmod>2026-10-17T23:26:14+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-exact-or-numerical-arc-length-methods/</loc>
		<lastmod>2026-10-17T23:26:15+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometry-of-a-surface-of-revolution/</loc>
		<lastmod>2026-10-17T23:26:15+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-surface-area-from-frustum-bands/</loc>
		<lastmod>2026-10-17T23:26:16+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/revolving-a-graph-about-the-x-axis/</loc>
		<lastmod>2026-10-17T23:26:16+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/revolving-a-graph-about-the-y-axis/</loc>
		<lastmod>2026-10-17T23:26:17+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-the-graph-orientation-for-surface-area/</loc>
		<lastmod>2026-10-17T23:26:18+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/revolution-about-a-shifted-horizontal-axis/</loc>
		<lastmod>2026-10-17T23:26:18+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/revolution-about-a-shifted-vertical-axis/</loc>
		<lastmod>2026-10-17T23:26:19+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/computing-radius-to-an-oblique-axis/</loc>
		<lastmod>2026-10-17T23:26:19+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/rotating-coordinates-for-oblique-axis-surface-area/</loc>
		<lastmod>2026-10-17T23:26:20+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/vertical-tangencies-and-surface-area-setups/</loc>
		<lastmod>2026-10-17T23:26:21+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/axis-crossings-and-overlapping-surfaces/</loc>
		<lastmod>2026-10-17T23:26:21+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/surface-area-of-cones-and-frustums/</loc>
		<lastmod>2026-10-17T23:26:22+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/cylinders-from-constant-radius-profiles/</loc>
		<lastmod>2026-10-17T23:26:22+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/generating-a-sphere-from-a-semicircle/</loc>
		<lastmod>2026-10-17T23:26:23+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/paraboloid-surface-area-from-power-profiles/</loc>
		<lastmod>2026-10-17T23:26:23+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/exponential-profiles-revolved-about-coordinate-axes/</loc>
		<lastmod>2026-10-17T23:26:24+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/matching-surface-areas-from-two-profile-descriptions/</loc>
		<lastmod>2026-10-17T23:26:24+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/surface-area-of-a-selected-curve-segment/</loc>
		<lastmod>2026-10-17T23:26:25+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/parametric-profiles-in-surface-area-integrals/</loc>
		<lastmod>2026-10-17T23:26:26+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/numerically-estimating-surface-areas/</loc>
		<lastmod>2026-10-17T23:26:26+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/diagnosing-surface-area-setup-errors/</loc>
		<lastmod>2026-10-17T23:26:27+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/surface-area-problems-with-coordinate-axes/</loc>
		<lastmod>2026-10-17T23:26:27+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/surface-area-problems-with-shifted-axes/</loc>
		<lastmod>2026-10-17T23:26:28+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/surface-area-problems-with-oblique-axes/</loc>
		<lastmod>2026-10-17T23:26:28+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-work-from-small-displacements/</loc>
		<lastmod>2026-10-17T23:26:29+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/constant-force-work-and-unit-conversion/</loc>
		<lastmod>2026-10-17T23:26:29+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/work-sign-and-direction-of-motion/</loc>
		<lastmod>2026-10-17T23:26:30+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/work-from-force-position-graphs/</loc>
		<lastmod>2026-10-17T23:26:31+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/setting-up-work-for-a-variable-force/</loc>
		<lastmod>2026-10-17T23:26:31+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/variable-forces-at-an-angle-to-motion/</loc>
		<lastmod>2026-10-17T23:26:32+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-hooke-s-law-for-a-spring/</loc>
		<lastmod>2026-10-17T23:26:32+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/work-to-stretch-or-compress-a-spring/</loc>
		<lastmod>2026-10-17T23:26:33+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/spring-work-and-external-work/</loc>
		<lastmod>2026-10-17T23:26:33+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/work-with-nonlinear-spring-laws/</loc>
		<lastmod>2026-10-17T23:26:34+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/lifting-objects-against-constant-gravity/</loc>
		<lastmod>2026-10-17T23:26:34+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/work-against-inverse-square-gravity/</loc>
		<lastmod>2026-10-17T23:26:35+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/lifting-a-cable-or-chain/</loc>
		<lastmod>2026-10-17T23:26:35+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/building-work-integrals-for-pumping-liquids/</loc>
		<lastmod>2026-10-17T23:26:36+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/pumping-liquid-from-a-cylindrical-tank/</loc>
		<lastmod>2026-10-17T23:26:36+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/pumping-liquid-from-a-conical-tank/</loc>
		<lastmod>2026-10-17T23:26:37+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/pumping-liquids-with-layered-density/</loc>
		<lastmod>2026-10-17T23:26:37+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/work-for-piecewise-force-laws/</loc>
		<lastmod>2026-10-17T23:26:38+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/work-against-position-dependent-resistance/</loc>
		<lastmod>2026-10-17T23:26:39+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/work-against-combined-forces/</loc>
		<lastmod>2026-10-17T23:26:39+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/work-and-potential-energy-in-one-dimension/</loc>
		<lastmod>2026-10-17T23:26:40+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-work-energy-theorem/</loc>
		<lastmod>2026-10-17T23:26:40+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/solving-work-problems-for-unknown-parameters/</loc>
		<lastmod>2026-10-17T23:26:41+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/mixed-work-integral-modeling-workshop/</loc>
		<lastmod>2026-10-17T23:26:41+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/common-errors-in-variable-force-work/</loc>
		<lastmod>2026-10-17T23:26:42+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/mass-from-continuous-density/</loc>
		<lastmod>2026-10-17T23:26:42+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/first-moments-about-coordinate-axes/</loc>
		<lastmod>2026-10-17T23:26:43+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-center-of-mass-of-a-lamina/</loc>
		<lastmod>2026-10-17T23:26:44+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/variable-density-rods/</loc>
		<lastmod>2026-10-17T23:26:44+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/uniform-rectangular-laminae/</loc>
		<lastmod>2026-10-17T23:26:45+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/setting-up-lamina-integrals-with-vertical-slices/</loc>
		<lastmod>2026-10-17T23:26:45+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/setting-up-lamina-integrals-with-horizontal-slices/</loc>
		<lastmod>2026-10-17T23:26:46+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-a-slice-direction/</loc>
		<lastmod>2026-10-17T23:26:46+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/density-depending-on-one-coordinate/</loc>
		<lastmod>2026-10-17T23:26:47+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/nonuniform-density-on-triangular-laminae/</loc>
		<lastmod>2026-10-17T23:26:47+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/centroids-of-regions-between-curves/</loc>
		<lastmod>2026-10-17T23:26:48+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/symmetry-and-centroid-simplification/</loc>
		<lastmod>2026-10-17T23:26:48+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/centroid-bounds-from-weighted-averages/</loc>
		<lastmod>2026-10-17T23:26:49+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/composite-laminae-and-mass-weighted-centroids/</loc>
		<lastmod>2026-10-17T23:26:49+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/laminae-with-holes-and-cutouts/</loc>
		<lastmod>2026-10-17T23:26:50+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/balancing-a-lamina-on-a-support/</loc>
		<lastmod>2026-10-17T23:26:50+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/density-proportional-to-distance-from-an-edge/</loc>
		<lastmod>2026-10-17T23:26:51+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/mass-of-solids-from-cross-sectional-slices/</loc>
		<lastmod>2026-10-17T23:26:51+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/first-moments-and-centroids-of-solids/</loc>
		<lastmod>2026-10-17T23:26:52+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/solids-with-density-varying-along-one-axis/</loc>
		<lastmod>2026-10-17T23:26:52+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/composite-solids-with-different-densities/</loc>
		<lastmod>2026-10-17T23:26:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/symmetry-in-three-dimensional-centers-of-mass/</loc>
		<lastmod>2026-10-17T23:26:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/checking-density-units-and-physical-plausibility/</loc>
		<lastmod>2026-10-17T23:26:54+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/common-errors-in-mass-and-centroid-integrals/</loc>
		<lastmod>2026-10-17T23:26:54+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/mixed-mass-moment-and-centroid-problems/</loc>
		<lastmod>2026-10-17T23:26:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/sequence-terms-and-indexing/</loc>
		<lastmod>2026-10-17T23:26:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/convergence-and-tail-behavior/</loc>
		<lastmod>2026-10-17T23:26:56+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/epsilon-n-proofs-by-choosing-an-index-bound/</loc>
		<lastmod>2026-10-17T23:27:21+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/uniqueness-of-sequence-limits/</loc>
		<lastmod>2026-10-17T23:27:22+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/sum-and-scalar-multiple-limit-laws/</loc>
		<lastmod>2026-10-17T23:27:23+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/product-and-quotient-limit-laws/</loc>
		<lastmod>2026-10-17T23:27:23+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/polynomial-sequence-limits/</loc>
		<lastmod>2026-10-17T23:27:24+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/rational-sequences-and-dominant-powers/</loc>
		<lastmod>2026-10-17T23:27:24+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/radical-sequence-limits-by-conjugation/</loc>
		<lastmod>2026-10-17T23:27:25+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-squeeze-theorem-for-sequences/</loc>
		<lastmod>2026-10-17T23:27:25+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/oscillating-factors-and-squeeze-bounds/</loc>
		<lastmod>2026-10-17T23:27:26+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/sine-and-cosine-limits-at-reciprocal-inputs/</loc>
		<lastmod>2026-10-17T23:27:26+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/exponential-decay-versus-polynomial-growth/</loc>
		<lastmod>2026-10-17T23:27:27+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-growth-versus-power-growth/</loc>
		<lastmod>2026-10-17T23:27:27+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-exponential-limit-1-x-n-n/</loc>
		<lastmod>2026-10-17T23:27:28+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/continuous-functions-of-convergent-sequences/</loc>
		<lastmod>2026-10-17T23:27:28+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/absolute-value-and-maximum-limit-laws/</loc>
		<lastmod>2026-10-17T23:27:29+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/nonconvergence-from-subsequences/</loc>
		<lastmod>2026-10-17T23:27:29+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/alternating-and-parity-defined-sequences/</loc>
		<lastmod>2026-10-17T23:27:30+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/fixed-point-equations-for-recursive-limits/</loc>
		<lastmod>2026-10-17T23:27:30+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/convergence-of-linear-recurrences/</loc>
		<lastmod>2026-10-17T23:27:31+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/nested-radical-sequence-limits/</loc>
		<lastmod>2026-10-17T23:27:31+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/exponential-and-logarithmic-limits-at-vanishing-inputs/</loc>
		<lastmod>2026-10-17T23:27:32+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/mixed-algebraic-and-transcendental-limit-problems/</loc>
		<lastmod>2026-10-17T23:27:32+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/epsilon-n-proofs-for-rational-sequences/</loc>
		<lastmod>2026-10-17T23:27:33+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/monotone-sequences-and-their-order/</loc>
		<lastmod>2026-10-17T23:27:33+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/upper-bounds-lower-bounds-and-boundedness/</loc>
		<lastmod>2026-10-17T23:27:34+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/proving-monotone-convergence-with-suprema/</loc>
		<lastmod>2026-10-17T23:27:35+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/what-numerical-terms-can-and-cannot-show/</loc>
		<lastmod>2026-10-17T23:27:35+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-monotone-convergence-theorem/</loc>
		<lastmod>2026-10-17T23:27:35+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/proving-monotonicity-with-consecutive-differences/</loc>
		<lastmod>2026-10-17T23:27:36+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/proving-monotonicity-with-ratios/</loc>
		<lastmod>2026-10-17T23:27:36+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/comparing-consecutive-terms-in-recursive-sequences/</loc>
		<lastmod>2026-10-17T23:27:37+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/induction-for-recursive-bounds/</loc>
		<lastmod>2026-10-17T23:27:37+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/invariant-intervals-for-recurrence-maps/</loc>
		<lastmod>2026-10-17T23:27:37+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/order-preserving-recurrence-maps/</loc>
		<lastmod>2026-10-17T23:27:38+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/proving-monotonicity-and-boundedness-together/</loc>
		<lastmod>2026-10-17T23:27:38+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/limits-of-recursively-defined-sequences/</loc>
		<lastmod>2026-10-17T23:27:39+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-the-correct-fixed-point/</loc>
		<lastmod>2026-10-17T23:27:40+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-recurrence-x-n-1-sqrt-2-x-n/</loc>
		<lastmod>2026-10-17T23:27:40+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/newton-iteration-for-square-roots/</loc>
		<lastmod>2026-10-17T23:27:41+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/convergence-of-affine-recurrences/</loc>
		<lastmod>2026-10-17T23:27:41+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/decreasing-recurrences-and-infimum-bounds/</loc>
		<lastmod>2026-10-17T23:27:42+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/eventual-monotonicity-and-convergence/</loc>
		<lastmod>2026-10-17T23:27:42+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-bounded-sequence-that-does-not-converge/</loc>
		<lastmod>2026-10-17T23:27:43+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/decreasing-recurrence-maps-and-oscillation/</loc>
		<lastmod>2026-10-17T23:27:43+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-recurrence-x-n-1-x-n-1-x-n/</loc>
		<lastmod>2026-10-17T23:27:44+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/fixed-point-equations-that-do-not-prove-convergence/</loc>
		<lastmod>2026-10-17T23:27:44+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-workshop-on-monotone-recursive-sequences/</loc>
		<lastmod>2026-10-17T23:27:45+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/common-errors-in-monotone-sequence-proofs/</loc>
		<lastmod>2026-10-17T23:27:45+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/sigma-notation-for-finite-sums/</loc>
		<lastmod>2026-10-17T23:27:46+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/partial-sums-and-their-indexing/</loc>
		<lastmod>2026-10-17T23:27:47+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/infinite-series-as-limits-of-partial-sums/</loc>
		<lastmod>2026-10-17T23:27:47+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/terms-partial-sums-and-series-values/</loc>
		<lastmod>2026-10-17T23:27:47+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/convergence-through-the-partial-sum-sequence/</loc>
		<lastmod>2026-10-17T23:27:48+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/reading-a-series-from-a-partial-sum-formula/</loc>
		<lastmod>2026-10-17T23:27:49+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-finite-geometric-sum-formula/</loc>
		<lastmod>2026-10-17T23:27:49+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/infinite-geometric-series-from-partial-sums/</loc>
		<lastmod>2026-10-17T23:27:50+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-series-with-a-general-first-term/</loc>
		<lastmod>2026-10-17T23:27:50+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/index-shifts-in-geometric-series/</loc>
		<lastmod>2026-10-17T23:27:51+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/negative-ratios-and-oscillating-geometric-sums/</loc>
		<lastmod>2026-10-17T23:27:52+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-series-at-unit-magnitude-ratios/</loc>
		<lastmod>2026-10-17T23:27:52+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-tails-and-omitted-terms/</loc>
		<lastmod>2026-10-17T23:27:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/repeating-decimals-as-geometric-series/</loc>
		<lastmod>2026-10-17T23:27:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/solving-for-parameters-in-geometric-series/</loc>
		<lastmod>2026-10-17T23:27:54+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/telescoping-finite-sums-by-cancellation/</loc>
		<lastmod>2026-10-17T23:27:54+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/infinite-telescoping-series-as-partial-sum-limits/</loc>
		<lastmod>2026-10-17T23:27:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/reciprocal-products-that-telescope/</loc>
		<lastmod>2026-10-17T23:27:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shifted-reciprocal-differences/</loc>
		<lastmod>2026-10-17T23:27:56+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/partial-fractions-for-telescoping-series/</loc>
		<lastmod>2026-10-17T23:27:56+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/telescoping-sums-with-multiple-residual-terms/</loc>
		<lastmod>2026-10-17T23:27:57+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/finding-a-telescoping-decomposition/</loc>
		<lastmod>2026-10-17T23:27:58+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/finite-versus-infinite-geometric-sums/</loc>
		<lastmod>2026-10-17T23:27:58+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/common-indexing-errors-in-series-sums/</loc>
		<lastmod>2026-10-17T23:27:59+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-and-telescoping-sum-workshop/</loc>
		<lastmod>2026-10-17T23:27:59+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-series-terms-must-approach-zero/</loc>
		<lastmod>2026-10-17T23:28:00+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/proving-divergence-from-a-nonzero-term-limit/</loc>
		<lastmod>2026-10-17T23:28:00+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/unbounded-terms-and-the-nth-term-test/</loc>
		<lastmod>2026-10-17T23:28:01+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/oscillating-terms-with-no-limit/</loc>
		<lastmod>2026-10-17T23:28:01+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-a-zero-term-limit-proves-nothing-about-convergence/</loc>
		<lastmod>2026-10-17T23:28:02+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-harmonic-series-as-a-vanishing-term-counterexample/</loc>
		<lastmod>2026-10-17T23:28:03+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/nth-term-test-workshop-with-mixed-term-formulas/</loc>
		<lastmod>2026-10-17T23:28:03+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/recognizing-geometric-series-from-constant-ratios/</loc>
		<lastmod>2026-10-17T23:28:04+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-geometric-partial-sum-formula/</loc>
		<lastmod>2026-10-17T23:28:04+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/convergence-of-geometric-series-with-ratios-below-one/</loc>
		<lastmod>2026-10-17T23:28:05+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/boundary-geometric-series-with-ratios-one-and-minus-one/</loc>
		<lastmod>2026-10-17T23:28:05+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-series-with-ratios-outside-the-unit-interval/</loc>
		<lastmod>2026-10-17T23:28:06+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/algebraically-disguised-geometric-series/</loc>
		<lastmod>2026-10-17T23:28:06+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-series-with-shifted-indices-and-starting-terms/</loc>
		<lastmod>2026-10-17T23:28:07+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/telescoping-series-as-differences-of-consecutive-terms/</loc>
		<lastmod>2026-10-17T23:28:08+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/telescoping-rational-terms-by-partial-fractions/</loc>
		<lastmod>2026-10-17T23:28:08+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/telescoping-reciprocal-products-with-a-fixed-index-gap/</loc>
		<lastmod>2026-10-17T23:28:09+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/factorial-terms-that-collapse-by-cancellation/</loc>
		<lastmod>2026-10-17T23:28:09+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/convergence-from-the-boundary-terms-of-a-telescoping-sum/</loc>
		<lastmod>2026-10-17T23:28:09+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/telescoping-series-workshop-with-finite-remainders/</loc>
		<lastmod>2026-10-17T23:28:10+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/classifying-p-series-from-their-exponents/</loc>
		<lastmod>2026-10-17T23:28:11+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-p-series-converge-when-the-exponent-exceeds-one/</loc>
		<lastmod>2026-10-17T23:28:11+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-p-series-diverge-when-the-exponent-is-at-most-one/</loc>
		<lastmod>2026-10-17T23:28:12+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shifted-p-series-and-constant-multipliers/</loc>
		<lastmod>2026-10-17T23:28:12+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/distinguishing-geometric-and-p-series-term-patterns/</loc>
		<lastmod>2026-10-17T23:28:13+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/positive-term-series-and-order/</loc>
		<lastmod>2026-10-17T23:28:13+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/integral-test-conditions-and-conclusion/</loc>
		<lastmod>2026-10-17T23:28:14+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-integral-test-with-rectangle-bounds/</loc>
		<lastmod>2026-10-17T23:28:14+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/verifying-eventual-decrease-before-integration/</loc>
		<lastmod>2026-10-17T23:28:15+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/p-series-threshold-from-improper-integrals/</loc>
		<lastmod>2026-10-17T23:28:15+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-factors-in-harmonic-type-series/</loc>
		<lastmod>2026-10-17T23:28:16+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/iterated-logarithms-and-borderline-convergence/</loc>
		<lastmod>2026-10-17T23:28:17+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shifting-indices-in-integral-test-applications/</loc>
		<lastmod>2026-10-17T23:28:17+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/direct-comparison-for-convergence/</loc>
		<lastmod>2026-10-17T23:28:18+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/integral-test-bounds-for-series-remainders/</loc>
		<lastmod>2026-10-17T23:28:18+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/direct-comparison-for-divergence/</loc>
		<lastmod>2026-10-17T23:28:19+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/proof-of-the-direct-comparison-convergence-rule/</loc>
		<lastmod>2026-10-17T23:28:19+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/why-lower-bounds-prove-divergence/</loc>
		<lastmod>2026-10-17T23:28:20+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/building-useful-termwise-inequalities/</loc>
		<lastmod>2026-10-17T23:28:20+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/rational-terms-compared-with-p-series/</loc>
		<lastmod>2026-10-17T23:28:21+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/radical-denominators-and-p-series-comparisons/</loc>
		<lastmod>2026-10-17T23:28:21+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-terms-compared-by-elementary-bounds/</loc>
		<lastmod>2026-10-17T23:28:22+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/exponential-denominators-and-geometric-bounds/</loc>
		<lastmod>2026-10-17T23:28:23+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/comparing-sums-with-multiple-simple-bounds/</loc>
		<lastmod>2026-10-17T23:28:23+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/common-errors-in-integral-and-direct-comparison/</loc>
		<lastmod>2026-10-17T23:28:24+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/integral-test-workshop-power-and-logarithm-tails/</loc>
		<lastmod>2026-10-17T23:28:24+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/direct-comparison-workshop-rational-sequences/</loc>
		<lastmod>2026-10-17T23:28:25+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/divergence-comparison-workshop-harmonic-lower-bounds/</loc>
		<lastmod>2026-10-17T23:28:25+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/choosing-between-integration-and-direct-comparison/</loc>
		<lastmod>2026-10-17T23:28:26+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/mixed-convergence-and-divergence-problems/</loc>
		<lastmod>2026-10-17T23:28:26+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/limit-comparison-with-a-finite-positive-limit/</loc>
		<lastmod>2026-10-17T23:28:27+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/limit-comparison-with-zero-or-infinite-limits/</loc>
		<lastmod>2026-10-17T23:28:27+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/asymptotic-equivalence-and-series-behavior/</loc>
		<lastmod>2026-10-17T23:28:28+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/products-and-quotients-of-asymptotic-equivalents/</loc>
		<lastmod>2026-10-17T23:28:28+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-a-power-law-comparison-model/</loc>
		<lastmod>2026-10-17T23:28:29+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/rational-functions-with-unequal-degrees/</loc>
		<lastmod>2026-10-17T23:28:30+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/equal-degree-polynomial-ratios-and-limit-constants/</loc>
		<lastmod>2026-10-17T23:28:30+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/radicals-of-polynomial-expressions/</loc>
		<lastmod>2026-10-17T23:28:31+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-factors-away-from-the-critical-power/</loc>
		<lastmod>2026-10-17T23:28:32+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-harmonic-logarithmic-threshold/</loc>
		<lastmod>2026-10-17T23:28:32+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/iterated-logarithmic-thresholds/</loc>
		<lastmod>2026-10-17T23:28:33+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-powers-dominate-logarithms/</loc>
		<lastmod>2026-10-17T23:28:33+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/dominant-terms-in-sums-of-positive-sequences/</loc>
		<lastmod>2026-10-17T23:28:34+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/cancellation-pitfalls-in-asymptotic-comparison/</loc>
		<lastmod>2026-10-17T23:28:34+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/close-radicals-and-rationalization/</loc>
		<lastmod>2026-10-17T23:28:35+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/small-angle-trigonometric-terms/</loc>
		<lastmod>2026-10-17T23:28:35+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-and-exponential-small-argument-equivalents/</loc>
		<lastmod>2026-10-17T23:28:36+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/fixed-shifts-and-constant-multipliers/</loc>
		<lastmod>2026-10-17T23:28:36+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/leading-order-equivalents-from-factored-expressions/</loc>
		<lastmod>2026-10-17T23:28:37+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/mixed-power-and-logarithm-comparison-models/</loc>
		<lastmod>2026-10-17T23:28:37+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/sums-with-competing-growth-scales/</loc>
		<lastmod>2026-10-17T23:28:38+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/computing-useful-comparison-ratios/</loc>
		<lastmod>2026-10-17T23:28:39+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/worked-comparisons-for-rational-and-radical-terms/</loc>
		<lastmod>2026-10-17T23:28:39+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/worked-comparisons-for-logarithmic-terms/</loc>
		<lastmod>2026-10-17T23:28:40+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/diagnosing-limit-comparison-decisions/</loc>
		<lastmod>2026-10-17T23:28:40+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/anatomy-of-an-alternating-series/</loc>
		<lastmod>2026-10-17T23:28:41+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-alternating-series-test/</loc>
		<lastmod>2026-10-17T23:28:42+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/proof-by-even-and-odd-partial-sums/</loc>
		<lastmod>2026-10-17T23:28:42+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/checking-decrease-and-the-zero-limit/</loc>
		<lastmod>2026-10-17T23:28:43+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/when-decrease-begins-after-the-first-term/</loc>
		<lastmod>2026-10-17T23:28:43+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/alternating-series-with-rational-terms/</loc>
		<lastmod>2026-10-17T23:28:44+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/alternating-p-series-classification/</loc>
		<lastmod>2026-10-17T23:28:44+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/when-the-alternating-series-test-is-inconclusive/</loc>
		<lastmod>2026-10-17T23:28:45+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-alternating-series-remainder-bound/</loc>
		<lastmod>2026-10-17T23:28:45+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-sign-of-the-alternating-series-error/</loc>
		<lastmod>2026-10-17T23:28:46+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-a-truncation-index-for-a-tolerance/</loc>
		<lastmod>2026-10-17T23:28:47+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/numerical-estimates-from-alternating-tails/</loc>
		<lastmod>2026-10-17T23:28:47+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/absolute-convergence-and-magnitude-series/</loc>
		<lastmod>2026-10-17T23:28:48+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/conditional-convergence-in-harmonic-type-series/</loc>
		<lastmod>2026-10-17T23:28:48+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-factors-in-alternating-series/</loc>
		<lastmod>2026-10-17T23:28:49+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/comparison-tests-for-absolute-convergence/</loc>
		<lastmod>2026-10-17T23:28:49+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/proof-of-rearrangement-invariance/</loc>
		<lastmod>2026-10-17T23:28:50+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/factorial-terms-and-absolute-convergence/</loc>
		<lastmod>2026-10-17T23:28:50+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-conditional-series-depend-on-order/</loc>
		<lastmod>2026-10-17T23:28:51+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/rearranging-the-alternating-harmonic-series/</loc>
		<lastmod>2026-10-17T23:28:51+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/grouping-terms-in-absolutely-convergent-series/</loc>
		<lastmod>2026-10-17T23:28:52+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/alternation-versus-mere-sign-changes/</loc>
		<lastmod>2026-10-17T23:28:52+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/classifying-mixed-alternating-series-examples/</loc>
		<lastmod>2026-10-17T23:28:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/pitfalls-in-alternating-series-error-estimates/</loc>
		<lastmod>2026-10-17T23:28:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-certified-approximation-workshop/</loc>
		<lastmod>2026-10-17T23:28:54+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/computing-successive-term-limits-for-the-ratio-test/</loc>
		<lastmod>2026-10-17T23:28:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/simplifying-nth-roots-for-the-root-test/</loc>
		<lastmod>2026-10-17T23:28:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-the-ratio-test-works/</loc>
		<lastmod>2026-10-17T23:28:56+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-the-root-test-works/</loc>
		<lastmod>2026-10-17T23:28:56+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/factorial-ratios-with-shifted-indices/</loc>
		<lastmod>2026-10-17T23:28:57+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/series-with-a-single-factorial-in-the-denominator/</loc>
		<lastmod>2026-10-17T23:28:57+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/products-and-quotients-of-factorials/</loc>
		<lastmod>2026-10-17T23:28:58+00:00</lastmod>
	</url>
	<url>
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		<lastmod>2026-10-17T23:28:58+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/fixed-bases-raised-to-the-index/</loc>
		<lastmod>2026-10-17T23:28:59+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/variable-bases-raised-to-the-index/</loc>
		<lastmod>2026-10-17T23:28:59+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/binomial-coefficient-series-and-the-ratio-test/</loc>
		<lastmod>2026-10-17T23:29:00+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/factorial-powers-and-terms-involving-n-to-the-n/</loc>
		<lastmod>2026-10-17T23:29:00+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-polynomial-decay-defeats-both-tests/</loc>
		<lastmod>2026-10-17T23:29:01+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-factors-at-the-ratio-test-boundary/</loc>
		<lastmod>2026-10-17T23:29:01+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/when-the-ratio-test-is-stronger-than-the-root-test/</loc>
		<lastmod>2026-10-17T23:29:02+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-ratio-test-with-limit-superior/</loc>
		<lastmod>2026-10-17T23:29:02+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-root-test-with-limit-superior/</loc>
		<lastmod>2026-10-17T23:29:03+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/finding-parameter-thresholds-with-the-ratio-test/</loc>
		<lastmod>2026-10-17T23:29:04+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/finding-parameter-thresholds-with-the-root-test/</loc>
		<lastmod>2026-10-17T23:29:04+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/using-ratio-and-root-tests-for-absolute-convergence/</loc>
		<lastmod>2026-10-17T23:29:05+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/when-a-ratio-or-root-limit-proves-divergence/</loc>
		<lastmod>2026-10-17T23:29:05+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-between-the-ratio-and-root-tests/</loc>
		<lastmod>2026-10-17T23:29:06+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/simplifying-terms-before-applying-ratio-and-root-tests/</loc>
		<lastmod>2026-10-17T23:29:06+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/avoiding-index-and-exponent-errors-in-convergence-tests/</loc>
		<lastmod>2026-10-17T23:29:07+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-mixed-workshop-on-ratio-root-and-test-selection/</loc>
		<lastmod>2026-10-17T23:29:07+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/the-definition-of-a-power-series/</loc>
		<lastmod>2026-10-17T23:29:08+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/reading-centers-and-coefficients-from-notation/</loc>
		<lastmod>2026-10-17T23:29:09+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/writing-powers-relative-to-the-center/</loc>
		<lastmod>2026-10-17T23:29:09+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-every-power-series-converges-at-its-center/</loc>
		<lastmod>2026-10-17T23:29:10+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-term-test-away-from-the-center/</loc>
		<lastmod>2026-10-17T23:29:10+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-convergence-points-form-an-interval/</loc>
		<lastmod>2026-10-17T23:29:11+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/absolute-convergence-inside-and-divergence-outside-the-radius/</loc>
		<lastmod>2026-10-17T23:29:11+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/radius-interval-and-endpoint-notation/</loc>
		<lastmod>2026-10-17T23:29:12+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/zero-and-infinite-radii-of-convergence/</loc>
		<lastmod>2026-10-17T23:29:12+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-ratio-test-radius-formula/</loc>
		<lastmod>2026-10-17T23:29:13+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-root-test-and-cauchy-hadamard-formula/</loc>
		<lastmod>2026-10-17T23:29:13+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/computing-radius-from-consecutive-coefficients/</loc>
		<lastmod>2026-10-17T23:29:14+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/when-the-ratio-test-gives-no-radius/</loc>
		<lastmod>2026-10-17T23:29:15+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/polynomial-growth-in-the-coefficients/</loc>
		<lastmod>2026-10-17T23:29:15+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/factorial-coefficients-and-infinite-radius/</loc>
		<lastmod>2026-10-17T23:29:16+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-and-exponential-coefficient-sequences/</loc>
		<lastmod>2026-10-17T23:29:16+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-coefficient-signs-do-not-change-the-radius/</loc>
		<lastmod>2026-10-17T23:29:17+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/sparse-coefficients-and-radius-calculation/</loc>
		<lastmod>2026-10-17T23:29:17+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/power-series-centered-away-from-zero/</loc>
		<lastmod>2026-10-17T23:29:18+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/how-variable-scaling-changes-the-radius/</loc>
		<lastmod>2026-10-17T23:29:18+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/using-geometric-bounds-to-test-a-point/</loc>
		<lastmod>2026-10-17T23:29:19+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/turning-a-power-series-point-test-into-a-series-test/</loc>
		<lastmod>2026-10-17T23:29:19+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-worked-workshop-on-finding-radii/</loc>
		<lastmod>2026-10-17T23:29:20+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/from-radius-to-a-candidate-convergence-interval/</loc>
		<lastmod>2026-10-17T23:29:20+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/common-errors-in-radius-and-interval-calculations/</loc>
		<lastmod>2026-10-17T23:29:21+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/why-radius-tests-do-not-decide-boundary-convergence/</loc>
		<lastmod>2026-10-17T23:29:21+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/substituting-the-two-endpoints-into-a-power-series/</loc>
		<lastmod>2026-10-17T23:29:22+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/testing-the-two-endpoints-independently/</loc>
		<lastmod>2026-10-17T23:29:22+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-term-test-at-power-series-boundaries/</loc>
		<lastmod>2026-10-17T23:29:23+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-series-at-their-boundary-points/</loc>
		<lastmod>2026-10-17T23:29:23+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/p-series-coefficients-at-the-endpoints/</loc>
		<lastmod>2026-10-17T23:29:24+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-corrections-to-harmonic-boundary-series/</loc>
		<lastmod>2026-10-17T23:29:25+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/alternation-created-by-the-left-endpoint/</loc>
		<lastmod>2026-10-17T23:29:25+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/alternating-series-remainders-at-a-boundary/</loc>
		<lastmod>2026-10-17T23:29:26+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/absolute-and-conditional-endpoint-convergence/</loc>
		<lastmod>2026-10-17T23:29:27+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/ratio-and-root-tests-at-radius-boundaries/</loc>
		<lastmod>2026-10-17T23:29:27+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/direct-comparison-for-endpoint-series/</loc>
		<lastmod>2026-10-17T23:29:28+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/limit-comparison-for-boundary-coefficients/</loc>
		<lastmod>2026-10-17T23:29:28+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/integral-tests-for-logarithmic-boundary-series/</loc>
		<lastmod>2026-10-17T23:29:29+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/central-binomial-coefficients-at-the-endpoints/</loc>
		<lastmod>2026-10-17T23:29:29+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/generalized-binomial-series-at-both-boundaries/</loc>
		<lastmod>2026-10-17T23:29:30+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shifted-centers-and-rescaled-boundary-terms/</loc>
		<lastmod>2026-10-17T23:29:31+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/endpoint-convergence-after-differentiation/</loc>
		<lastmod>2026-10-17T23:29:31+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/endpoint-convergence-after-integration/</loc>
		<lastmod>2026-10-17T23:29:32+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/telescoping-terms-at-a-power-series-boundary/</loc>
		<lastmod>2026-10-17T23:29:32+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/asymptotic-coefficients-and-endpoint-verdicts/</loc>
		<lastmod>2026-10-17T23:29:33+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/parity-and-symmetry-in-endpoint-behavior/</loc>
		<lastmod>2026-10-17T23:29:33+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/common-errors-in-boundary-substitution/</loc>
		<lastmod>2026-10-17T23:29:34+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/writing-the-exact-interval-of-convergence/</loc>
		<lastmod>2026-10-17T23:29:34+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-complete-endpoint-analysis-workshop/</loc>
		<lastmod>2026-10-17T23:29:35+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/adding-and-scaling-power-series-at-a-common-center/</loc>
		<lastmod>2026-10-17T23:29:35+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/aligning-coefficients-in-sparse-power-series/</loc>
		<lastmod>2026-10-17T23:29:36+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/why-sums-preserve-the-smaller-radius/</loc>
		<lastmod>2026-10-17T23:34:16+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-cauchy-product-formula/</loc>
		<lastmod>2026-10-17T23:34:17+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/computing-product-coefficients-by-convolution/</loc>
		<lastmod>2026-10-17T23:34:17+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/multiplication-by-the-centered-variable/</loc>
		<lastmod>2026-10-17T23:34:18+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/product-radii-and-coefficient-cancellation/</loc>
		<lastmod>2026-10-17T23:34:19+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/squaring-a-power-series/</loc>
		<lastmod>2026-10-17T23:34:19+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-termwise-differentiation-theorem/</loc>
		<lastmod>2026-10-17T23:34:20+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/calculating-coefficients-after-differentiation/</loc>
		<lastmod>2026-10-17T23:34:20+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/why-differentiation-keeps-the-radius/</loc>
		<lastmod>2026-10-17T23:34:21+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/recovering-coefficients-from-derivatives/</loc>
		<lastmod>2026-10-17T23:34:21+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/repeated-differentiation-and-falling-factorials/</loc>
		<lastmod>2026-10-17T23:34:22+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/the-termwise-integration-theorem/</loc>
		<lastmod>2026-10-17T23:34:22+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/antiderivative-coefficients-and-constants/</loc>
		<lastmod>2026-10-17T23:34:23+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-integration-keeps-the-radius/</loc>
		<lastmod>2026-10-17T23:34:23+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/definite-integrals-on-interior-intervals/</loc>
		<lastmod>2026-10-17T23:34:24+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/the-product-rule-from-cauchy-product-coefficients/</loc>
		<lastmod>2026-10-17T23:34:24+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/integrating-products-through-convolution/</loc>
		<lastmod>2026-10-17T23:34:25+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/undoing-differentiation-and-integration/</loc>
		<lastmod>2026-10-17T23:34:25+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/parity-patterns-under-power-series-operations/</loc>
		<lastmod>2026-10-17T23:34:26+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/evaluating-series-operations-at-interior-points/</loc>
		<lastmod>2026-10-17T23:34:26+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/truncating-series-before-and-after-operations/</loc>
		<lastmod>2026-10-17T23:34:27+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/common-errors-in-power-series-operations/</loc>
		<lastmod>2026-10-17T23:34:27+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/mixed-power-series-operations-workshop/</loc>
		<lastmod>2026-10-17T23:34:28+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/the-geometric-series-and-its-remainder/</loc>
		<lastmod>2026-10-17T23:34:29+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/shifting-and-scaling-geometric-series/</loc>
		<lastmod>2026-10-17T23:34:29+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/rational-functions-with-distinct-linear-factors/</loc>
		<lastmod>2026-10-17T23:34:30+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/repeated-linear-factors-and-geometric-products/</loc>
		<lastmod>2026-10-17T23:34:30+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/quadratic-denominators-as-geometric-expansions/</loc>
		<lastmod>2026-10-17T23:34:31+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/choosing-expansion-centers-for-rational-functions/</loc>
		<lastmod>2026-10-17T23:34:31+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/cauchy-products-and-convolution-coefficients/</loc>
		<lastmod>2026-10-17T23:34:32+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/coefficient-patterns-from-products-of-geometric-factors/</loc>
		<lastmod>2026-10-17T23:34:32+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/reciprocals-of-power-series-by-coefficient-recursion/</loc>
		<lastmod>2026-10-17T23:34:33+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/quotients-by-normalizing-the-denominator/</loc>
		<lastmod>2026-10-17T23:34:34+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/composing-functions-inside-a-geometric-series/</loc>
		<lastmod>2026-10-17T23:34:34+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/domain-checks-before-substituting-into-a-series/</loc>
		<lastmod>2026-10-17T23:34:35+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-logarithm-series-from-the-geometric-series/</loc>
		<lastmod>2026-10-17T23:34:35+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-arctangent-series-from-the-geometric-series/</loc>
		<lastmod>2026-10-17T23:34:36+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/logarithm-series-under-scaling-and-shifting/</loc>
		<lastmod>2026-10-17T23:34:36+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/finding-limits-from-leading-series-terms/</loc>
		<lastmod>2026-10-17T23:34:37+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/resolving-cancellations-in-series-based-limits/</loc>
		<lastmod>2026-10-17T23:34:37+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/geometric-and-weighted-geometric-sums/</loc>
		<lastmod>2026-10-17T23:34:38+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-sums-from-power-series-substitution/</loc>
		<lastmod>2026-10-17T23:34:39+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/odd-power-sums-from-arctangent-representations/</loc>
		<lastmod>2026-10-17T23:34:39+00:00</lastmod>
	</url>
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		<lastmod>2026-10-17T23:34:40+00:00</lastmod>
	</url>
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		<lastmod>2026-10-17T23:34:40+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/logarithmic-integrals-and-their-associated-sums/</loc>
		<lastmod>2026-10-17T23:34:41+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/building-series-representations-for-composite-rational-functions/</loc>
		<lastmod>2026-10-17T23:34:41+00:00</lastmod>
	</url>
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		<loc>https://www.clinicalbiostats.com/tutorials/a-strategy-workshop-for-series-based-evaluation/</loc>
		<lastmod>2026-10-17T23:34:42+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-polynomial-definition-and-notation/</loc>
		<lastmod>2026-10-17T23:34:42+00:00</lastmod>
	</url>
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		<lastmod>2026-10-17T23:34:43+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:43+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:44+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/computing-a-taylor-polynomial-from-derivative-data/</loc>
		<lastmod>2026-10-17T23:34:44+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/linearization-as-a-tangent-line-approximation/</loc>
		<lastmod>2026-10-17T23:34:45+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:45+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:46+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-polynomials-for-the-exponential-function/</loc>
		<lastmod>2026-10-17T23:34:46+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/maclaurin-polynomials-for-sine/</loc>
		<lastmod>2026-10-17T23:34:47+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/maclaurin-polynomials-for-cosine/</loc>
		<lastmod>2026-10-17T23:34:47+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/sine-and-cosine-polynomials-at-nonzero-centers/</loc>
		<lastmod>2026-10-17T23:34:48+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-polynomials-for-the-natural-logarithm/</loc>
		<lastmod>2026-10-17T23:34:48+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:49+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-polynomials-for-real-powers/</loc>
		<lastmod>2026-10-17T23:34:49+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/exact-taylor-polynomials-for-polynomial-functions/</loc>
		<lastmod>2026-10-17T23:34:50+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/symmetry-and-vanishing-taylor-coefficients/</loc>
		<lastmod>2026-10-17T23:34:50+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:51+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-polynomials-of-sums-and-scalar-multiples/</loc>
		<lastmod>2026-10-17T23:34:52+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-polynomials-of-products/</loc>
		<lastmod>2026-10-17T23:34:52+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-polynomials-of-compositions/</loc>
		<lastmod>2026-10-17T23:34:53+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-polynomials-of-quotients/</loc>
		<lastmod>2026-10-17T23:34:53+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:54+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:54+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/common-taylor-polynomial-calculation-errors/</loc>
		<lastmod>2026-10-17T23:34:55+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-coefficients-from-derivatives/</loc>
		<lastmod>2026-10-17T23:34:56+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:56+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/maclaurin-series-for-sine-and-cosine/</loc>
		<lastmod>2026-10-17T23:34:57+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/translating-exponential-and-trigonometric-taylor-series/</loc>
		<lastmod>2026-10-17T23:34:58+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:58+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:58+00:00</lastmod>
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		<lastmod>2026-10-17T23:34:59+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/the-arctangent-series-from-termwise-integration/</loc>
		<lastmod>2026-10-17T23:34:59+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:00+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/termwise-differentiation-and-integration-as-construction-tools/</loc>
		<lastmod>2026-10-17T23:35:00+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-series-for-logarithms-about-positive-centers/</loc>
		<lastmod>2026-10-17T23:35:01+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:02+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:03+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:03+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:04+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/products-of-taylor-series-by-coefficient-convolution/</loc>
		<lastmod>2026-10-17T23:35:04+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:05+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/the-tangent-series-from-a-differential-identity/</loc>
		<lastmod>2026-10-17T23:35:05+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-series-for-rational-functions-near-regular-points/</loc>
		<lastmod>2026-10-17T23:35:06+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/square-root-taylor-series-about-positive-centers/</loc>
		<lastmod>2026-10-17T23:35:06+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/a-smooth-function-whose-taylor-series-misses-its-values/</loc>
		<lastmod>2026-10-17T23:35:07+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/proving-taylor-series-identities-with-differential-equations/</loc>
		<lastmod>2026-10-17T23:35:07+00:00</lastmod>
	</url>
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		<loc>https://www.clinicalbiostats.com/tutorials/endpoint-behavior-after-termwise-differentiation-and-integration/</loc>
		<lastmod>2026-10-17T23:35:08+00:00</lastmod>
	</url>
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		<loc>https://www.clinicalbiostats.com/tutorials/mixed-taylor-construction-for-logarithmic-and-radical-products/</loc>
		<lastmod>2026-10-17T23:35:08+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/choosing-valid-expansions-for-composite-functions/</loc>
		<lastmod>2026-10-17T23:35:09+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/the-taylor-remainder-as-an-approximation-error/</loc>
		<lastmod>2026-10-17T23:35:09+00:00</lastmod>
	</url>
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		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-lagrange-remainder-bound/</loc>
		<lastmod>2026-10-17T23:35:10+00:00</lastmod>
	</url>
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		<loc>https://www.clinicalbiostats.com/tutorials/the-hypotheses-behind-lagrange-s-bound/</loc>
		<lastmod>2026-10-17T23:35:10+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/bounding-the-highest-derivative/</loc>
		<lastmod>2026-10-17T23:35:11+00:00</lastmod>
	</url>
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		<loc>https://www.clinicalbiostats.com/tutorials/choosing-taylor-degree-from-a-factorial-bound/</loc>
		<lastmod>2026-10-17T23:35:11+00:00</lastmod>
	</url>
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		<loc>https://www.clinicalbiostats.com/tutorials/exponential-approximation-with-lagrange-bounds/</loc>
		<lastmod>2026-10-17T23:35:12+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/sine-and-cosine-errors-from-derivative-bounds/</loc>
		<lastmod>2026-10-17T23:35:12+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/bounding-errors-for-logarithms-near-one/</loc>
		<lastmod>2026-10-17T23:35:13+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/alternating-series-remainder-bound/</loc>
		<lastmod>2026-10-17T23:35:13+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/why-alternating-remainders-have-predictable-signs/</loc>
		<lastmod>2026-10-17T23:35:14+00:00</lastmod>
	</url>
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		<loc>https://www.clinicalbiostats.com/tutorials/checking-the-conditions-for-alternating-error-bounds/</loc>
		<lastmod>2026-10-17T23:35:15+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/selecting-degree-with-the-first-omitted-term/</loc>
		<lastmod>2026-10-17T23:35:15+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/comparing-lagrange-and-alternating-series-bounds/</loc>
		<lastmod>2026-10-17T23:35:15+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:16+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:16+00:00</lastmod>
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		<loc>https://www.clinicalbiostats.com/tutorials/tightening-derivative-bounds-for-taylor-errors/</loc>
		<lastmod>2026-10-17T23:35:17+00:00</lastmod>
	</url>
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		<lastmod>2026-10-17T23:35:18+00:00</lastmod>
	</url>
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		<loc>https://www.clinicalbiostats.com/tutorials/taylor-error-estimates-for-nonzero-centers/</loc>
		<lastmod>2026-10-17T23:35:18+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:21+00:00</lastmod>
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		<lastmod>2026-10-17T23:35:23+00:00</lastmod>
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	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/high-order-taylor-methods-for-initial-value-problems/</loc>
		<lastmod>2026-10-17T23:35:33+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/recurrence-relations-for-ode-taylor-coefficients/</loc>
		<lastmod>2026-10-17T23:35:34+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/adaptive-step-sizes-from-taylor-error-estimates/</loc>
		<lastmod>2026-10-17T23:35:34+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/stability-of-taylor-based-ode-integrators/</loc>
		<lastmod>2026-10-17T23:35:35+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/worked-error-diagnosis-for-initial-value-solvers/</loc>
		<lastmod>2026-10-17T23:35:35+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/parametric-equations-and-plane-curves/</loc>
		<lastmod>2026-10-17T23:35:36+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/parameter-domains-and-curve-traces/</loc>
		<lastmod>2026-10-17T23:35:37+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/sketching-parametric-curves-with-tables/</loc>
		<lastmod>2026-10-17T23:35:37+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/eliminating-parameters-without-losing-branches/</loc>
		<lastmod>2026-10-17T23:35:38+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/orientation-of-a-parametrized-curve/</loc>
		<lastmod>2026-10-17T23:35:38+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/reparametrizing-a-curve/</loc>
		<lastmod>2026-10-17T23:35:39+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-parametric-slope-formula/</loc>
		<lastmod>2026-10-17T23:35:39+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/tangent-lines-at-regular-parameter-values/</loc>
		<lastmod>2026-10-17T23:35:40+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/horizontal-tangents-in-parametric-curves/</loc>
		<lastmod>2026-10-17T23:35:40+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/vertical-tangents-in-parametric-curves/</loc>
		<lastmod>2026-10-17T23:35:41+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/regular-points-and-the-derivative-pair/</loc>
		<lastmod>2026-10-17T23:35:41+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-second-derivative-formula/</loc>
		<lastmod>2026-10-17T23:35:42+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/computing-second-derivatives-parametrically/</loc>
		<lastmod>2026-10-17T23:35:43+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/concavity-of-parametrized-curves/</loc>
		<lastmod>2026-10-17T23:35:43+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/inflection-points-on-parametric-curves/</loc>
		<lastmod>2026-10-17T23:35:44+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/cusps-and-other-singular-parameter-values/</loc>
		<lastmod>2026-10-17T23:35:44+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/speed-along-a-parametrized-curve/</loc>
		<lastmod>2026-10-17T23:35:44+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/how-reparametrization-changes-speed/</loc>
		<lastmod>2026-10-17T23:35:45+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/tangents-to-parametrized-circles-and-ellipses/</loc>
		<lastmod>2026-10-17T23:35:45+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/tangent-analysis-for-polynomial-parametrizations/</loc>
		<lastmod>2026-10-17T23:35:46+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/tangencies-and-concavity-on-cycloid-type-curves/</loc>
		<lastmod>2026-10-17T23:35:46+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/repeated-points-and-self-intersections/</loc>
		<lastmod>2026-10-17T23:35:47+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/tangent-directions-at-self-intersections/</loc>
		<lastmod>2026-10-17T23:35:47+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/a-worked-parametric-curve-analysis/</loc>
		<lastmod>2026-10-17T23:35:48+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/position-displacement-and-distance-along-a-parametric-path/</loc>
		<lastmod>2026-10-17T23:35:49+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/common-errors-in-parametric-differentiation/</loc>
		<lastmod>2026-10-17T23:35:49+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-arc-length-from-chord-sums/</loc>
		<lastmod>2026-10-17T23:35:50+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/speed-from-parametric-derivatives/</loc>
		<lastmod>2026-10-17T23:35:50+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/arc-length-for-cartesian-parametric-curves/</loc>
		<lastmod>2026-10-17T23:35:51+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/arc-length-functions-and-accumulated-distance/</loc>
		<lastmod>2026-10-17T23:35:51+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/why-arc-length-is-invariant-under-reparameterization/</loc>
		<lastmod>2026-10-17T23:35:52+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/constructing-an-arc-length-parameter/</loc>
		<lastmod>2026-10-17T23:35:52+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/regularity-stops-and-piecewise-arc-length/</loc>
		<lastmod>2026-10-17T23:35:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/velocity-vectors-speed-and-direction-of-motion/</loc>
		<lastmod>2026-10-17T23:35:53+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/tangential-and-normal-components-of-acceleration/</loc>
		<lastmod>2026-10-17T23:35:54+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/constant-speed-motion-and-orthogonal-acceleration/</loc>
		<lastmod>2026-10-17T23:35:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/time-rescaling-and-reversal-of-motion/</loc>
		<lastmod>2026-10-17T23:35:55+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/straight-line-motion-with-changing-speed/</loc>
		<lastmod>2026-10-17T23:35:56+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/uniform-circular-motion-speed-and-acceleration/</loc>
		<lastmod>2026-10-17T23:35:56+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/elliptical-motion-under-uniform-angular-speed/</loc>
		<lastmod>2026-10-17T23:35:57+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/projectile-motion-from-position-functions/</loc>
		<lastmod>2026-10-17T23:35:57+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/cycloid-arc-length-and-motion/</loc>
		<lastmod>2026-10-17T23:35:58+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/polynomial-paths-an-arc-length-workshop/</loc>
		<lastmod>2026-10-17T23:35:58+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/trigonometric-paths-a-speed-and-length-workshop/</loc>
		<lastmod>2026-10-17T23:35:59+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/piecewise-trajectories-stops-and-total-distance/</loc>
		<lastmod>2026-10-17T23:36:00+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/common-errors-in-parametric-arc-length-calculations/</loc>
		<lastmod>2026-10-17T23:36:00+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/average-velocity-and-average-speed-on-a-parametric-interval/</loc>
		<lastmod>2026-10-17T23:36:01+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/prescribing-speed-along-a-fixed-path/</loc>
		<lastmod>2026-10-17T23:36:01+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/velocity-and-acceleration-for-polynomial-position-models/</loc>
		<lastmod>2026-10-17T23:36:02+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/diagnosing-motion-from-position-velocity-and-acceleration/</loc>
		<lastmod>2026-10-17T23:36:03+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/defining-and-plotting-polar-coordinates/</loc>
		<lastmod>2026-10-17T23:36:03+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/converting-polar-coordinates-to-cartesian-coordinates/</loc>
		<lastmod>2026-10-17T23:36:04+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/converting-cartesian-equations-to-polar-form/</loc>
		<lastmod>2026-10-17T23:36:05+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/equivalent-polar-coordinates/</loc>
		<lastmod>2026-10-17T23:36:05+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/plotting-points-with-negative-radius/</loc>
		<lastmod>2026-10-17T23:36:06+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/angle-periodicity-and-coordinate-aliases/</loc>
		<lastmod>2026-10-17T23:36:06+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/building-polar-graphs-from-key-values/</loc>
		<lastmod>2026-10-17T23:36:07+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/symmetry-tests-for-polar-curves/</loc>
		<lastmod>2026-10-17T23:36:07+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/circles-centered-at-the-pole/</loc>
		<lastmod>2026-10-17T23:36:08+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/polar-lines-and-constant-angle-rays/</loc>
		<lastmod>2026-10-17T23:36:08+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/circles-offset-from-the-pole/</loc>
		<lastmod>2026-10-17T23:36:09+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/lima-ons-and-their-loop-types/</loc>
		<lastmod>2026-10-17T23:36:09+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/cardioids-as-a-special-lima-on/</loc>
		<lastmod>2026-10-17T23:36:10+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/rose-curves-and-petal-counts/</loc>
		<lastmod>2026-10-17T23:36:10+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/lemniscates-in-polar-form/</loc>
		<lastmod>2026-10-17T23:36:11+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/archimedean-spirals/</loc>
		<lastmod>2026-10-17T23:36:12+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/polar-equations-of-conics/</loc>
		<lastmod>2026-10-17T23:36:12+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/classifying-polar-conics-by-eccentricity/</loc>
		<lastmod>2026-10-17T23:36:13+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-focus-directrix-equation/</loc>
		<lastmod>2026-10-17T23:36:13+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/orienting-and-sketching-polar-conics/</loc>
		<lastmod>2026-10-17T23:36:14+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-polar-symmetry-criteria/</loc>
		<lastmod>2026-10-17T23:36:14+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/finding-fundamental-periods-of-polar-curves/</loc>
		<lastmod>2026-10-17T23:36:15+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/multiple-traces-and-repeated-curve-points/</loc>
		<lastmod>2026-10-17T23:36:15+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/workshop-on-sketching-standard-polar-families/</loc>
		<lastmod>2026-10-17T23:36:16+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/diagnosing-common-polar-graphing-errors/</loc>
		<lastmod>2026-10-17T23:36:17+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-polar-slope-formula/</loc>
		<lastmod>2026-10-17T23:36:17+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/polar-tangent-vectors-and-direction/</loc>
		<lastmod>2026-10-17T23:36:18+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/horizontal-and-vertical-tangencies-in-polar-form/</loc>
		<lastmod>2026-10-17T23:36:18+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/tangent-lines-at-the-pole/</loc>
		<lastmod>2026-10-17T23:36:19+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/cusps-and-singular-tangent-parameters/</loc>
		<lastmod>2026-10-17T23:36:20+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/tangent-lines-to-standard-polar-curves/</loc>
		<lastmod>2026-10-17T23:36:20+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/diagnosing-tangency-errors-in-polar-coordinates/</loc>
		<lastmod>2026-10-17T23:36:21+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/tangents-at-self-intersections-of-polar-curves/</loc>
		<lastmod>2026-10-17T23:36:21+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/choosing-bounds-that-trace-a-region-once/</loc>
		<lastmod>2026-10-17T23:36:22+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-polar-area-formula/</loc>
		<lastmod>2026-10-17T23:36:22+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/area-of-a-single-polar-loop/</loc>
		<lastmod>2026-10-17T23:36:23+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/areas-of-petals-in-rose-curves/</loc>
		<lastmod>2026-10-17T23:36:23+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/area-of-an-inner-loop/</loc>
		<lastmod>2026-10-17T23:36:24+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/area-between-radially-nested-polar-curves/</loc>
		<lastmod>2026-10-17T23:36:24+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/finding-polar-curve-intersections/</loc>
		<lastmod>2026-10-17T23:36:25+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/identifying-the-outer-curve-between-intersections/</loc>
		<lastmod>2026-10-17T23:36:26+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/common-area-of-two-polar-regions/</loc>
		<lastmod>2026-10-17T23:36:26+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/overlap-area-workshop-for-intersecting-curves/</loc>
		<lastmod>2026-10-17T23:36:27+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/deriving-the-polar-arc-length-formula/</loc>
		<lastmod>2026-10-17T23:36:27+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/arc-length-of-cardioids-and-limacons/</loc>
		<lastmod>2026-10-17T23:36:27+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/arc-length-of-rose-curves/</loc>
		<lastmod>2026-10-17T23:36:28+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/arc-length-of-an-archimedean-spiral/</loc>
		<lastmod>2026-10-17T23:36:29+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/arc-length-near-cusps-and-pole-crossings/</loc>
		<lastmod>2026-10-17T23:36:29+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/diagnosing-polar-area-and-arc-length-setups/</loc>
		<lastmod>2026-10-17T23:36:30+00:00</lastmod>
	</url>
	<url>
		<loc>https://www.clinicalbiostats.com/tutorials/integrated-polar-analysis-of-a-lemniscate/</loc>
		<lastmod>2026-10-17T23:36:30+00:00</lastmod>
	</url>
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