$\lim_{x \rightarrow 0}{\frac{d}{dx}\int_{}^{}\frac{1 - \cos x}{x^{2}}}dx$ is equal to

Question

Dr. Abubacker · Accepted Answer

(c)
$\lim_{x \rightarrow 0}{\frac{d}{dx}\int_{}^{}\left( \frac{1 - \cos x}{x^{2}} \right)}dx = \lim_{x \rightarrow 0}\frac{1 - \cos x}{x^{2}}$
$= \lim_{x \rightarrow 0}\frac{2\sin^{2}{x/2}}{{4.x}^{2}/4}$
$= \frac{1}{2}{\lim_{x \rightarrow 0}\left( \frac{\sin\frac{x}{2}}{\frac{x}{2}} \right)}^{2} = \frac{1}{2}$

Q. $\lim_{x \rightarrow 0}{\frac{d}{dx}\int_{}^{}\frac{1 - \cos x}{x^{2}}}dx$ is equal to

Explanation

Reviewed by Dr. Abubacker

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