Common Core · AP Calculus AB
LIM-1.D
AP Calculus AB, Unit 1 — Determine the limits of functions using limit theorems.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
The 3 skills that cover it
- LimitsDescribe what a function approaches near a point, even where it is undefined, using tables, graphs and algebra.Read the lesson →
- Infinite Limits & AsymptotesRead a vertical asymptote as a one-sided limit that grows without bound, a horizontal asymptote as a limit at infinity, and tell an asymptote from a hole — for rational, radical and exponential forms.Read the lesson →
- Limit Laws & the Formal DefinitionWork with limits as objects: combine known limits with the limit laws, rationalise a radical quotient, use the two special trigonometric limits and the squeeze theorem, and read the epsilon-delta definition on a straight line.Read the lesson →
What a student should be able to do
- Estimate a limit from a table or a graph.
- Evaluate a limit by direct substitution when the function is continuous.
- Resolve a 0/0 form by factoring and cancelling.
- Describe one-sided limits and limits at infinity.
- Evaluate a one-sided limit at a vertical asymptote and say which way it grows.
- Find the vertical asymptotes of a rational function, and tell them from holes.
- Evaluate a limit at infinity by comparing degrees or dividing by the highest power.
- Write the horizontal asymptote of a rational, radical or exponential function as a limit.
- Combine given limits with the sum, product, quotient, root and composition laws, and say when the quotient law does not apply.
- Resolve a 0/0 form by rationalising a radical, clearing a complex fraction or splitting an absolute value.
- Use sin(x)/x and (1 - cos x)/x, and the squeeze theorem, to find a limit.
- Find the delta that answers a given epsilon for a linear function.