Let g(x)= cases x^ 2 -4 x-2 , & x 2 k, & x=2 cases Find the value of so that is…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let g(x)={x2−4x−2,x≠2k,x=2g(x)=\begin{cases}\dfrac{x^{2}-4}{x-2}, & x\ne2\\ k, & x=2\end{cases} Find the value of kk so that gg is differentiable at x=2x=2.

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