Question

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

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

Answer 1

Answer: (B)

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