lim _x arrow 0 √fracx-sin xx+sin^2 x is equal to

Correct answer: (B) 0. lim _x arrow 0 √fracx-sin xx+sin^2 x=lim _x arrow 0 √frac1-(sin x)/x1+fracsin^2 xx =lim _x arrow 0 √((1-(sin x)/x)/(1+ ((sin x)/x ) sin x))=√((1-1)/(1+1 × 0))=0

Q84 / 125 · BITSAT 2021 · Mathematics

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

A
1
Correct answer
B
0
C
$\infty$
D
None of these

Solution

$\lim _{x \rightarrow 0} \sqrt{\frac{x-\sin x}{x+\sin ^{2} x}=\lim _{x \rightarrow 0} \sqrt{\frac{1-\frac{\sin x}{x}}{1+\frac{\sin ^{2} x}{x}}}}$ $=\lim _{x \rightarrow 0} \sqrt{\frac{1-\frac{\sin x}{x}}{1+\left(\frac{\sin x}{x}\right) \sin x}}=\sqrt{\frac{1-1}{1+1 \times 0}}=0$

Hence, the correct answer is option: 'B'.

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

Solution

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