Let be the function defined by f(x)= cases 3x+k, & x<2

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let ff be the function defined by f(x)={3x+k,x<2,kx2−8,x≥2.f(x)= \begin{cases} 3x+k, & x<2,\\ kx^{2}-8, & x\ge 2. \end{cases} Determine the value of kk for which lim⁡x→2f(x)\displaystyle\lim_{x\to 2} f(x) exists.

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