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Let $f(x)=|sin x|$,then

\[\begin{array}{1 1}(A)\;f \;is\;everywhere\;differentiable\\(B)\;f \;is\;everywhere\;continuous\;but\;not\;differentiable\;at\;x=n\pi,n\in z \\(C)\;f\;is\;everywhere\;continuous\;but\;not\;differentiable\;at\;x=(2n+1)\frac{\pi}{2},n\in z\\(D)\;none\;of\;these\end{array} \]

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Toolbox:
  • General solution for $x$ in $\sin x$ is $x=n\pi+(-1)\alpha,n\in z$
$f(x)=\mid \sin x\mid$
The general solution for $\sin x$ is $x=n\pi+(-1)\alpha,n\in z$
Hence $f(x)=\mid \sin x\mid$ is continuous everywhere but not differentiable at $x=n\pi,n\in z$
Hence the correct option is $B$
answered Jul 4, 2013 by sreemathi.v
 

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