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 ?

IIT JAM MS - 2022
IIT JAM MS

Updated On: Oct 1, 2024

$f(\frac{2}{\pi})=1$
$f(\frac{1}{\pi})=\frac{1}{\pi}$
$f(-\frac{2}{\pi})=-1$
f is not continuous at x = 0

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The Correct Option is B

Solution and Explanation

The correct option is (B) :

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

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The Correct Option is B

Solution and Explanation

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