Differentiation Question 329
Question: The derivative of function $ f(x) $ is $ {{\tan }^{4}}x $ . If $ f(0)=0 $ then $ \underset{x\to 0}{\mathop{\lim }}\frac{f(x)}{x} $ is equal to
[J & K 2005]
Options:
A) 1
B) 0
C) -1
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \underset{x\to 0}{\mathop{\lim }}\frac{f(x)}{x}=\underset{x\to 0}{\mathop{\lim }}\frac{f(x)-0}{x-0}=\underset{x\to 0}{\mathop{\lim }}\frac{f(x)-f(0)}{x-0} $
$ ={{. {f}’(x) |} _{x=0}} $
$ ={{. {{\tan }^{4}}x |} _{x=0}}=0 $
BETA
