_ x 0 x e^2- x x is equal to - Vidyadip

MCQ

$\lim _{x \rightarrow 0} \frac{x e^2-\sin x}{x}$ is equal to

A
1
B
2
C
3
✓
$0$

✓

Answer

Correct option: D.

$0$

(D)
$\lim _{x \rightarrow 0} \frac{x e ^x-\sin x}{x}=\lim _{x \rightarrow 0}\left( e ^x-\frac{\sin x}{x}\right)$
$= e ^0-1$
$=1-1$
$=0$

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