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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; \[f\left( x \right) = \begin{cases}kx + 1, if & x \leq 5 \\ 3x - 5, if & x > 5\end{cases}\] at x = 5
Solution
Given :
We have
(LHL at x = 5) =
(RHL at x = 5) =
If f(x) is continuous at x = 5, then
\[\lim_{x \to 5^-} f\left( x \right) = \lim_{x \to 5^+} f\left( x \right)\]
\[ \Rightarrow 5k + 1 = 10\]
\[ \Rightarrow k = \frac{9}{5}\]
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