If f (x)= cc x x + x, & x 0 2, & x=0 ., then - Vidyadip

MCQ

If $f (x)=\left\{\begin{array}{cc}\frac{\sin x}{x}+\cos x, & x \neq 0 \\ 2, & x=0\end{array}\right.$, then

A
$f (x)$ is discontinuous at $x=0$
B
$\lim _{x \rightarrow 0} f (x)=1$
✓
$f (x)$ is continuous at $x=0$
D
none of these

✓

Answer

Correct option: C.

$f (x)$ is continuous at $x=0$

(C)
$\lim _{x \rightarrow 0} f(x)=\lim _{x \rightarrow 0}\left(\frac{\sin x}{x}+\cos x\right)$
$\therefore f (x)$ is continuous at $x=0$

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