Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question

AP Calculus ABmediummcq1 pt

Let $f(x)=\begin{cases} kx+1, & x<2 \\ x^2, & x\ge 2 \end{cases}$ . For what value of $k$ is $f$ continuous at $x=2$ ?

A.

2

B.

3

C.

4

D.

\frac{3}{2}

Explanation

Core Concept

Continuity requires $2k+1=2^2=4$ . Solving gives $2k=3$ , so $k=\frac{3}{2}$ .

Correct Answer

D $\frac{3}{2}$

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