Common Core · AP Calculus AB

LIM-2.B

AP Calculus AB, Unit 1 — Determine intervals over which a function is continuous.

A note on this mapping: The Common Core has no calculus standards; this is the AP Calculus AB learning objective.

The skill that covers it

Continuity & DiscontinuitiesDecide whether a function is continuous at a point with the three conditions, name the kind of break where it is not, choose the constant that mends a piecewise rule, and use the Intermediate Value Theorem to promise a root.Read the lesson →

What a student should be able to do

Test continuity at a point: f(a) exists, the limit exists, and the two agree.
Classify a discontinuity as removable, a jump or infinite, from a rule or a graph.
Find the constant that makes a piecewise function continuous.
Apply the Intermediate Value Theorem to locate a root on an interval.

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