Question:

Let f : RR\R→\R be the function defined by
f(x)={limh0(x+h)sin(1x+h)xsin1xhx00,x=0f(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 ?

Updated On: Oct 1, 2024
  • f(2π)=1f(\frac{2}{\pi})=1
  • f(1π)=1πf(\frac{1}{\pi})=\frac{1}{\pi}
  • f(2π)=1f(-\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(1π)=1πf(\frac{1}{\pi})=\frac{1}{\pi}.
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