Functions Question 218
Question: The value of $ \underset{a\to 0}{\mathop{\lim }},\frac{\sin a-\tan a}{{{\sin }^{3}}a} $ will be
[UPSEAT 1999]
Options:
A) $ -\frac{1}{2} $
B) $ \frac{1}{2} $
C) 1
D) ?1
Show Answer
Answer:
Correct Answer: A
Solution:
$ \underset{a\to 0}{\mathop{\lim }},\frac{\sin a-\tan a}{{{\sin }^{3}}a}=\underset{a\to 0}{\mathop{\lim }},\frac{\cos a-1}{{{\sin }^{2}}a\cos a}=\underset{a\to 0}{\mathop{\lim }},\frac{-(1-\cos a)}{(1-{{\cos }^{2}}a)(\cos a)} $ $ =\underset{a\to 0}{\mathop{\lim }},[ -\frac{1}{(1+\cos a)\cos a} ]=-\frac{1}{(1+1)1}=\frac{-1}{2} $ $ $
BETA
