Common Core · AP Calculus AB
LIM-2.D
AP Calculus AB, Unit 1 — Interpret the behaviour of functions using limits involving infinity.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
AP Calculus AB, Unit 1 — Interpret the behaviour of functions using limits involving infinity: vertical and horizontal asymptotes.
A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.
The 2 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 →
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.