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 ?
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 ?
\(f(x)=\begin{cases} \lim\limits_{h \rightarrow0}\frac{(x+h)\sin(\frac{1}{x}+h)-x\sin\frac{1}{x}}{h} & x \ne 0\\ 0, & x=0\end{cases}\)
Then which one of the following statements is NOT true ?
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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