Limits and Continuity Multiple Choice
This topic covers limits from tables, graphs, algebraic forms, one-sided limits, infinite behavior, continuity, and the Intermediate Value Theorem.
How to study for AP Calculus AB
Build every answer around the representation, operation, interval, units, and justification the prompt is actually asking for.
Core concepts
Concept 1
Limits and Continuity Multiple Choice questions test AP Calculus AB reasoning with limits, derivatives, integrals, rates, accumulation, and justifications.
Exam cue: Name the task: evaluate a limit, differentiate, interpret a derivative, analyze behavior, integrate, solve a differential equation, or justify a conclusion.
Concept 2
The strongest answer identifies the representation, operation, interval, condition, and requested quantity before calculating.
Exam cue: Check notation, domain, units, graph behavior, calculator permission, interval endpoints, and whether the response asks for value, rate, area, or accumulation.
Concept 3
Eliminate choices that use the right formula on the wrong function, interval, units, sign, or endpoint behavior.
Exam cue: Use exact values and symbolic reasoning when required; use calculator output only when the section permits and the setup is correct.
Risk pitfalls and guardrails
Solving a nearby problem while missing the quantity named in the stem.
Guardrail: Use a 15-second safety pause before finalizing your action.
Forgetting that derivative, integral, average rate, average value, and net change answer different questions.
Guardrail: Use a 15-second safety pause before finalizing your action.
Giving a numerical answer without the sign, units, interval, or justification needed by the prompt.
Guardrail: Use a 15-second safety pause before finalizing your action.
Memory anchors
Limit
A limit describes the value a function approaches as the input approaches a point.
One-Sided Limit
A one-sided limit follows the function from only the left or only the right.
Continuity
Continuity at a point requires the function value, limit, and equality between them.
Removable Discontinuity
A removable discontinuity occurs when a hole prevents continuity but the limit exists.
Jump Discontinuity
A jump discontinuity occurs when one-sided limits are finite but unequal.
Infinite Limit
An infinite limit describes unbounded output near an input value.
Squeeze Theorem
The Squeeze Theorem traps a function between two functions with the same limit.
Intermediate Value
The Intermediate Value Theorem guarantees values between endpoint outputs for continuous functions.
Asymptote
An asymptote describes behavior approached by a graph rather than necessarily reached.
Limit Algebra
Limit algebra works only when the operations are valid for the functions involved.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Evaluate lim as x approaches 3 of (x^2 - 9)/(x - 3).
Evaluate lim as x approaches 0 of (sin(5x))/x.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
What is Pass Harbor?
Completely free exam prep for 317 U.S. exams.
- Practice questions
- Flashcards
- Study guides
- Mock exams
- No registration
- No paywall
- Start instantly
“No more expensive exam prep. Quality study tools should be accessible to everyone.”