AP Calculus ABmediummcq1 pt

Let $f(x)=\dfrac{1}{(x-2)^2}$ . Which type of discontinuity does $f$ have at $x=2$ ?

A.Removable discontinuity

B.Infinite discontinuity

C.Jump discontinuity

D.No discontinuity;

f

is continuous at

x=2

Explanation

Core Concept

As $x\to 2$ from either side, $(x-2)^2\to 0^+$ , so $f(x)\to +\infty$ . The function has a vertical asymptote and an infinite discontinuity at $x=2$ .

Correct Answer

BInfinite discontinuity

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Let f(x)=1(x−2)2f(x)=\dfrac{1}{(x-2)^2}f(x)=(x−2)21​. Which type of discontinuity does fff have at x=2x=2x=2?

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Let $f(x)=\dfrac{1}{(x-2)^2}$ . Which type of discontinuity does $f$ have at $x=2$ ?