Functions Question 25
Question: $ \underset{x\to 0}{\mathop{\lim }}\frac{\sqrt{1+\sin x}-\sqrt{1-\sin x}}{x}= $
Options:
A) -1
B) 1
C) 2
D) -2
Show Answer
Answer:
Correct Answer: B
Solution:
Apply L-Hospital?s rule, $ \underset{x\to 0}{\mathop{\lim }}\frac{\sqrt{1+\sin x}-\sqrt{1-\sin x}}{x} $ $ =\underset{x\to 0}{\mathop{\lim }}\frac{\cos x}{2\sqrt{1+\sin x}}+\frac{\cos x}{2\sqrt{1-\sin x}}=\frac{1}{2}+\frac{1}{2}=1. $
BETA
