Functions Question 163
Question: $ \underset{x\to \infty }{\mathop{\lim }},\sqrt{\frac{x+\sin x}{x-\cos x}}= $
[Roorkee 1994]
Options:
A) 0
B) 1
C) ?1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to \infty }{\mathop{\lim }},\sqrt{( \frac{x+\sin x}{x-\cos x} )}=\underset{x\to \infty }{\mathop{\lim }}\sqrt{( \frac{1+\frac{\sin x}{x}}{1-\frac{\cos x}{x}} )}=\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]
BETA
