_ x x+ x x- x = - Vidyadip

MCQ

$\lim _{x \rightarrow \infty} \sqrt{\frac{x+\sin x}{x-\cos x}}=$

A
$0$
✓
1
C
-1
D
None of these

✓

Answer

Correct option: B.

1

(B)
$\lim _{x \rightarrow \infty} \sqrt{\left(\frac{x+\sin x}{x-\cos x}\right)}=\lim _{x \rightarrow \infty} \sqrt{\left(\frac{1+\frac{\sin x}{x}}{1-\frac{\cos x}{x}}\right)}$
$=\lim _{x \rightarrow \infty} \sqrt{1}=1$
$\ldots\left[\because \lim _{x \rightarrow \infty} \frac{\sin x}{x}=\lim _{x \rightarrow \infty} \frac{\cos x}{x}=0\right]$

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