Question

Let f : $\R→\R$ be the function defined by
$f(x)=\begin{cases} \lim\limits_{h \rightarrow0}\frac{(x+h)\sin(\frac{1}{x}+h)-x\sin\frac{1}{x}}{h} & x \ne 0\\\ 0, & x=0\end{cases}$
Then which one of the following statements is NOT true ?

• A. $f(\frac{2}{\pi})=1$
• B. $f(\frac{1}{\pi})=\frac{1}{\pi}$
• C. $f(-\frac{2}{\pi})=-1$
• D. f is not continuous at x = 0

Answer 1

Answer: (B)

$f(\frac{1}{\pi})=\frac{1}{\pi}$

Answer 2

The correct option is (B) : $f(\frac{1}{\pi})=\frac{1}{\pi}$.