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  • If the function f defined as <img alt="f(x) = \begin{Bmatrix} \frac{x^{2}-9}{x-3} ,&x\neq 3 \\ k,& x=3 \end{Bmatrix}" src="https://learn.careers360.com/latex-image/?f%28x%29%20%3D%20%5Cbegin%7BBmatrix%7D%20%5Cfrac%7Bx%5E%7B2%7D-9%7D%7Bx-3%7D%20

If the function f defined as f(x) = \begin{Bmatrix} \frac{x^{2}-9}{x-3} ,&x\neq 3 \\ k,& x=3 \end{Bmatrix} is continuous at x = 3, find the value of k.

 

Answers (1)

Given:

f(x) = \begin{Bmatrix} \frac{x^{2}-9}{x-3} ,&x\neq 3 \\ k,& x=3 \end{Bmatrix} is continuous at x = 3

\lim _{x \rightarrow 3^+} f(x) = \lim _{x \rightarrow 3^-} = f(3)

\\ \lim _{x \rightarrow 3^+} \frac{x^{2}-9}{x-3}=\lim _{x \rightarrow 3^-} \frac{x^{2}-9}{x-3} = k \\\\ \lim _{x \rightarrow 3^+} \frac{(x-3)(x+3)}{x-3} = k \\ \lim _{x \rightarrow 3^+} (x+3)= k \\ k =6

 

 

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Safeer PP

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