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

MCQ

$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{{x^2}}} - \,\cos \,x}}{{{{\sin }^2}\,x}}$ is equal to

A
$2$
B
$3$
✓
$\frac {3}{2}$
D
$\frac {5}{4}$

✓

Answer

Correct option: C.

$\frac {3}{2}$

c
$\mathop {\lim }\limits_{x \to 0} \frac{{2x{e^{{x^2}}} + \sin x}}{{2\sin x\cos x}}$

$\mathop {\lim }\limits_{x \to 0} \left( {\frac{x}{{\sin x}}{e^{{x^2}}} + \frac{1}{2}} \right)\frac{1}{{\cos x}} = 1 + \frac{1}{2} = \frac{3}{2}$

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