Unit overview
Weight4-7%
TopicsLimits and Continuity
Skillsrecall, application, exam reasoning
prep.worlddebatecollective.org
May 2026 exam cycleCalc BC notes
Study unitLimits and Continuity
WDC Prep tracks Limits and Continuity as a syllabus section with original notes, practice, and weak-topic repair.
Built around the official College Board AP Central course pages course structure, with WDC notes, drills, and review sets organized by unit.
AP Calculus BC: Limits and Continuity
Use limits to predict behavior near a point and continuity to decide whether substitution is legal.
Key Ideas
Check whether direct substitution works before switching techniques. If substitution fails, decide whether factoring, rationalizing, or one-sided analysis fits the expression. Continuity claims should always identify the function value and the limiting value together.
How to Use It
Write the reason a limit method works: factor because of a removable discontinuity, rationalize because of radicals, or compare one-sided values for jump behavior.
Formulas and Terms
lim as x->a f(x); continuous at a if limit equals function value
Common Mistakes
Treating undefined substitution as evidence that the limit does not exist. Forgetting that continuity is a three-part condition. Using a graph claim without matching it to algebraic behavior.
Linked Practice
Use the matching WDC original practice for Limits and Continuity to turn the note into retrieval and timed application.
AP Calculus BC Skill: One-Sided and Infinite Limits
One-Sided and Infinite Limits sits inside Limits and Continuity. This note turns the syllabus heading into the moves students actually need under timed conditions.
Key Ideas
One-Sided and Infinite Limits questions usually test one recognisable decision before they test calculation or recall. Check whether direct substitution works before switching techniques. If substitution fails, decide whether factoring, rationalizing, or one-sided analysis fits the expression.
How to Use It
Write the reason a limit method works: factor because of a removable discontinuity, rationalize because of radicals, or compare one-sided values for jump behavior. For One-Sided and Infinite Limits, write the evidence, formula, or grammar rule before choosing the final answer.
Formulas and Terms
lim as x->a f(x); continuous at a if limit equals function value
Common Mistakes
Treating undefined substitution as evidence that the limit does not exist. Forgetting that continuity is a three-part condition. Skipping the small setup step that makes One-Sided and Infinite Limits easy to check.
Linked Practice
Use the matching WDC original practice for Limits and Continuity to turn the note into retrieval and timed application.
AP Calculus BC Skill: Continuity and Removable Discontinuities
Continuity and Removable Discontinuities sits inside Limits and Continuity. This note turns the syllabus heading into the moves students actually need under timed conditions.
Key Ideas
Continuity and Removable Discontinuities questions usually test one recognisable decision before they test calculation or recall. Check whether direct substitution works before switching techniques. If substitution fails, decide whether factoring, rationalizing, or one-sided analysis fits the expression.
How to Use It
Write the reason a limit method works: factor because of a removable discontinuity, rationalize because of radicals, or compare one-sided values for jump behavior. For Continuity and Removable Discontinuities, write the evidence, formula, or grammar rule before choosing the final answer.
Formulas and Terms
lim as x->a f(x); continuous at a if limit equals function value
Common Mistakes
Treating undefined substitution as evidence that the limit does not exist. Forgetting that continuity is a three-part condition. Skipping the small setup step that makes Continuity and Removable Discontinuities easy to check.
Linked Practice
Use the matching WDC original practice for Limits and Continuity to turn the note into retrieval and timed application.