Exam Strategy

Calculus AB · AP · Limits and Continuity

CED focus

Connecting Multiple Representations of Limits

This topic is assessed on the AP Exam.

Multiple-choice tips

• Ask whether the limit is one-sided, two-sided, or DNE before computing.
• Decide one-sided vs two-sided limits from the stem before computing.
• Eliminate choices that confuse limit value with function value at a point.
• Use tables/graphs for estimates; algebra for exact limits.
• Watch for removable discontinuities in MC graphs.

Free-response tips

• Use ‘approaches’ language; cite IVT or continuity when justifying.
• Write limit notation correctly (approaches, not equals, when appropriate).
• Show algebraic limit laws or factoring that justifies the value.
• Cite continuity or IVT when the FRQ asks for justification.
• Connect a limit answer to a short interpretation (instantaneous rate setup).

Common traps

• Equating lim f(x) as x→a with f(a) when a hole exists
• Equating a limit to f(a) when there is a hole or jump
• Dropping one-sided limit information on piecewise graphs
• Treating infinity as a number you can plug in

Quick checklist

• [ ] Can evaluate a limit from a graph with correct one-sided language
• [ ] Can justify continuity or IVT on a closed interval
• [ ] Can use limit notation without swapping equals/approaches