Question

The derivative of function $ f(x) $ is $ {{\tan }^{4}}x $ . If $ f(x)=0, $ then $ \underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{x} $ is equal to

• A. $ 1 $
• B. $ 0 $
• C. $ -1 $
• D. none of these

Answer 1

Answer: (B)

Given, $ f(0)=0,\,\,f'(x)={{\tan }^{4}}x $
$ \therefore $ $ \underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{x}=\underset{x\to 0}{\mathop{\lim }}\,\frac{f'(x)}{1} $
$ =\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\tan }^{4}}x}{1}=0 $