Working with the Intermediate Value Theorem
Learn how to use the Intermediate Value Theorem to prove that a function reaches a value, with step-by-step AP Calculus examples and practice problems.
Using L’Hopital’s Rule for Indeterminate Forms (Preview)
A preview of L
The Limit Definition of
Understand where the number e comes from, how to use its limit definition, and how to evaluate limits involving e for AP Calculus AB & BC.
Selecting Procedures for Determining Limits
A practical AP Calculus guide to selecting the right procedure for determining limits, including direct substitution, algebraic manipulation, factoring, rationalization, and special trigonometric limits.
Removing Discontinuities
Learn how to remove a removable discontinuity by factoring, simplifying, and defining the function at the missing point. Includes worked AP Calculus examples and practice problems.
Practice Problem Set: Limits and Continuity
Practice limits and continuity for AP Calculus AB & BC with worked answers covering one-sided limits, algebraic limits, piecewise functions, continuity, and asymptotic behavior.
One-Sided Limits Explained
Learn how to evaluate left-hand and right-hand limits, determine when a two-sided limit exists, and connect one-sided limits to continuity and vertical asymptotes for AP Calculus AB & BC.
Limits of Piecewise Functions
Learn how to evaluate limits of piecewise functions by checking the correct branch, comparing one-sided limits, and determining when a two-sided limit exists for AP Calculus AB & BC.
Limits and Asymptotic Behavior of Rational Functions
Learn how to evaluate limits and determine asymptotic behavior of rational functions, including limits at infinity, vertical asymptotes, horizontal asymptotes, and indeterminate forms for AP Calculus AB & BC.
Limits Involving Trigonometric Functions
How to evaluate limits involving trigonometric functions using fundamental trig limits, algebraic manipulation, and the squeeze theorem for AP Calculus AB & BC.