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 $x=4$.
$f(x)=\left\{ \frac{x^2-16}{x-4}, x \neq 4 k, x=4 \right.$

A
$2$
B
$4$
C
$6$
✓
$8$

✓

Answer

Correct option: D.

$8$

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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