AP Calculus AB 1.13 Continuity & Discontinuities Review

Review AP Calculus AB 1.13 by connecting limits with continuity conditions, then practise choosing parameter values that remove a discontinuity when the function allows it.

Exam points

solve for constants that make a piecewise or rational function continuous at a hole
use the limiting value to define a missing point and remove a discontinuity

Covered syllabus points

LIM-2.C—Determine values of x or solve for parameters that make discontinuous functions continuous, if possible

[Maximum number: 1]

A function f(x) equals rt fraction numerator x squared end exponent minus x over denominator x minus 1 end fraction for all x except x=1. For the function to be continuous at x=1, the value of f(1) must be

$\infty$ egral from 0 to 1 of start fraction numerator

to the power of x end exponent over

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Covered syllabus points

1.13 Removing Discontinuities question 1