$\lim_{x ightarrow 0}\left\lbrack \frac{8\sin{x + x\cos x}}{3 an{x + x^{2}}} ight brack$ is equal to

Question

$\lim_{x ightarrow 0}\left\lbrack \frac{8\sin{x + x\cos x}}{3	an{x + x^{2}}} ightbrack$ is equal to

Dr. Abubacker · Accepted Answer

(a)
$\lim_{x ightarrow 0}\left\lbrack \frac{8\sin{x + x\cos x}}{3	an{x + x^{2}}} ightbrack = \lim_{x ightarrow 0}\left\lbrack \frac{\frac{{8\ sin}x}{x}{+ \cos x}}{\frac{{3\ tan}x}{x}{+ x}} ightbrack$
$= \frac{\lim_{x ightarrow 0}\left\lbrack \frac{{8\ sin}x}{x}{+ \cos x} ightbrack}{\lim_{x ightarrow 0}\ \left\lbrack \frac{{3\ tan}x}{x}{+ x} ightbrack}$
$= \frac{9}{3} = 3$

Q. $\lim_{x \rightarrow 0}\left\lbrack \frac{8\sin{x + x\cos x}}{3\tan{x + x^{2}}} \right\rbrack$ is equal to

Explanation

Reviewed by Dr. Abubacker

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