If f(x) = x^ 2 -25 x - 5 , k,& when x 5 when x = 5 is continuous … - Vidyadip

Question

If $\text{f(x)} = \begin{cases} \frac{\text{x}^{2}-25}{\text{x - 5}},\\\text{ }\text{ }\text{ }\text{ }\text{ }k,&\\ \end{cases}$$\quad \text{when x}\neq5\\\\\quad \text{when x = 5 }$is continuous at x = 5, find the value of k.

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Answer

For $\DeclareMathOperator*{\median}{\text{lim}} \median_{\text{x}\rightarrow5}\frac{\text{x}^{2}-25}{\text{x - 5}}=\DeclareMathOperator*{\median}{\text{lim}} \median_{\text{x}\rightarrow5}(\text{x + 5})=10$
$\therefore\text{k}=10$.

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