Functions Question 180
Question: The value of $ \underset{x\to 0}{\mathop{\lim }},\frac{\sqrt{1-\cos x^{2}}}{1-\cos x} $ is
Options:
A) $ \frac{1}{2} $
B) $ 2 $
C) $ \sqrt{2} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We have $ \underset{x\to 0}{\mathop{\lim }}\frac{\sqrt{1-\cos x^{2}}}{1-\cos x}=\underset{x\to 0}{\mathop{\lim }},\frac{\sqrt{2,{{\sin }^{2}}(x^{2}/2)}}{2,{{\sin }^{2}}(x/2)} $ $ =\frac{1}{\sqrt{2}},\underset{x\to 0}{\mathop{\lim }}( \frac{\frac{\sin ,(x^{2}/2)}{x^{2}/2}}{{{( \frac{\sin ,(x/2)}{x/2} )}^{2}}} ).\frac{x^{2}/2}{x^{2}/4}=\sqrt{2} $ .
BETA
