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Question
In each of the following, find the value of the constant k so that the given function is continuous at the indicated point; \[f\left( x \right) = \begin{cases}\frac{x^2 - 25}{x - 5}, & x \neq 5 \\ k , & x = 5\end{cases}\]at x = 5
Solution
If f(x) is continuous at x = 5, then
\[\lim_{x \to 5} f\left( x \right) = f\left( 5 \right)\]
\[ \Rightarrow \lim_{x \to 5} \left( x + 5 \right) = k\]
\[ \Rightarrow k = 5 + 5 = 10\]
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