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Question
If \[f\left( x \right) = \begin{cases}\frac{x^2 - 16}{x - 4}, & \text{ if } x \neq 4 \\ k , & \text{ if } x = 4\end{cases}\] is continuous at x = 4, find k.
Solution
Given: \[f\left( x \right) = \begin{cases}\frac{x^2 - 16}{x - 4}, & \text{ if } x \neq 4 \\ k , & \text{ if } x = 4\end{cases}\]
If \[f\left( x \right)\] is continuous at \[x = 4\] , then
\[ \Rightarrow \lim_{x \to 4} \left( x + 4 \right) = k\]
\[ \Rightarrow k = 8\]
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