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Determine the value for k that will make the function continuous at c = 4.

f(x)={x29x+3 if x4kx+5 if x>4f(x)=\left\{\begin{array}{ll}{\frac{x^{2}-9}{x+3}} & {\text { if } x \leq 4} \\ {k x+5} & {\text { if } x>4}\end{array}\right.


Answered 6 months ago
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So, by the definition, if the limx4f(x)\lim_{x\to4} f(x) and f(4)f(4) exists and

limx4f(x)=f(4)1\begin{aligned} \lim_{x\to4} f(x) & = f(4) & \rightarrow & \textcircled{1} \end{aligned}

then ff is continuous at c=4c=4

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