If f(x)= r x^4-16 x-2 , when x 2 16, when x=2 ., then - Vidyadip

MCQ

If $f(x)=\left\{\begin{array}{r}\frac{x^4-16}{x-2}, \text { when } x \neq 2 \\ 16, \text { when } x=2\end{array}\right.$, then

A
$f (x)$ is continuous at $x=2$
✓
$f (x)$ is discontinuous at $x=2$
C
$\lim _{x \rightarrow 2} f(x)=16$
D
None of these

✓

Answer

Correct option: B.

$f (x)$ is discontinuous at $x=2$

(B)
$\lim _{x \rightarrow 2} f (x)=\lim _{x \rightarrow 2} \frac{x^4-16}{x-2}$
$=\lim _{x \rightarrow 2} \frac{(x-2)(x+2)\left(x^2+4\right)}{x-2}$
$=\lim _{x \rightarrow 2}(x+2)\left(x^2+4\right)=32$ and $f(2)=16$
$\therefore \quad \lim _{x \rightarrow 2} f (x) \neq f (2)$
$\therefore f (x)$ is discontinuous at $x=2$.

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