Determine the value of k for which the function f(x) is continuou… - Vidyadip

MCQ

Determine the value of $k$ for which the function $f(x)$ is continuous at $x=4$.$f(x)= \begin{cases}\frac{x^2-16}{x-4}, & x \neq 4 \\ k, & x=4\end{cases}$

A
2
B
4
C
6
✓
8

✓

Answer

Correct option: D.

8

(d) : Since $f(x)$ is continuous at $x=4$. Therefore, $\lim _{x \rightarrow 4} f(x)=f(4)$
$\Rightarrow \lim _{x \rightarrow 4} f(x)=k \quad[\because f(4)=k]$
$\Rightarrow \lim _{x \rightarrow 4} \frac{x^2-16}{x-4}=k \Rightarrow \lim _{x \rightarrow 4} \frac{(x-4)(x+4)}{x-4}=k$
$\Rightarrow \lim _{x \rightarrow 4}(x+4)=k \Rightarrow k=8$

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