A function is defined by f(x)= cases kx+1, & x<2

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A function

f

is defined by

f(x)=\begin{cases} kx+1, & x<2,\\ x^{2}-k, & x\ge 2. \end{cases}

For which value of

k

does

\displaystyle \lim_{x\to 2} f(x)

exist? (a)

3

(b)

\dfrac{3}{2}

(c)

1

(d)

-1

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