A) 0
B) 1
C) ?1
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to \infty }{\mathop{\lim }}\,\,\,\sqrt{\left( \frac{x+\sin x}{x-\cos x} \right)}=\underset{x\to \infty }{\mathop{\lim }}\,\,\sqrt{\left( \frac{1+\frac{\sin x}{x}}{1-\frac{\cos x}{x}} \right)}=\underset{x\to \infty }{\mathop{\lim }}\,\sqrt{1}=1\] \[[\,\because \,\,\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{\sin x}{x}\] and \[\underset{x\to \infty }{\mathop{\lim }}\,\,\frac{\cos x}{x}\] both are equal to 0]
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