Let f(x)= cases x^ 2 -4 x-2 ,& x<2, +1,& x 2

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

Problem

Let f(x)={x2−4x−2,x<2,kx+1,x≥2.f(x)=\begin{cases}\dfrac{x^{2}-4}{x-2},& x<2,\\kx+1,& x\ge 2.\end{cases} Determine the value of kk for which lim⁡x→2f(x)\displaystyle\lim_{x\to2}f(x) exists. (a) 00 (b) 32\dfrac{3}{2} (c) 12\dfrac{1}{2} (d) 22

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