_ x 0 1- x ^2 x = - Vidyadip

MCQ

$\lim _{x \rightarrow 0} \frac{1-\cos x}{\tan ^2 x}=$

A
2
✓
$\frac{1}{2}$
C
3
D
$\frac{1}{3}$

✓

Answer

Correct option: B.

$\frac{1}{2}$

(B)
$\lim _{x \rightarrow 0} \frac{1-\cos k x}{x^2}=\frac{ k ^2}{2}$
$\lim _{x \rightarrow 0} \frac{1-\cos x}{\tan ^2 x}=\frac{\lim _{x \rightarrow 0} \frac{1-\cos x}{x^2}}{\lim _{x \rightarrow 0} \frac{\tan ^2 x}{x^2}}=\frac{\frac{1^2}{2}}{1^2}=\frac{1}{2}$

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