Mathematics

Problem

Let

g

be the function defined by

g(x)=\begin{cases}\dfrac{x^2-16}{x-4}, & x\ne 4,\\k, & x=4,\end{cases}

where

k

is a real constant. (a) Calculate

\displaystyle\lim_{x\to 4}g(x)

. (b) Determine the value of

k

that makes

g

continuous at

x=4

. (c) Verify your answer in part (b) by explicitly checking the three conditions for continuity at a point.