Functions Question 75
Question: $ \underset{h\to 0}{\mathop{\lim }}\frac{{{(a+h)}^{2}}\sin (a+h)-a^{2}\sin a}{h}= $
[IIT 1989]
Options:
A) $ a\cos a+a^{2}\sin a $
B) $ a\sin a+a^{2}\cos a $
C) $ 2a\sin a+a^{2}\cos a $
D) $ 2a\cos a+a^{2}\sin a $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{d}{da}[a^{2}\sin a]=2a\sin a+a^{2}\cos a. $ Aliter : Apply L-Hospital?s rule, $ \underset{h\to 0}{\mathop{\lim }}\frac{{{(a+h)}^{2}}\sin (a+h)-a^{2}\sin a}{h} $ $ =\underset{h\to 0}{\mathop{\lim }}\frac{2(a+h)\sin (a+h)+{{(a+h)}^{2}}\cos (a+h)}{1} $ $ =2a\sin a+a^{2}\cos a. $
BETA
