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Question

Let f(x)=|sinx|. Then which of the following statement(s) is/are true?

A
f is everywhere differentiable
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B
f is not differentiable at x=nπ, nZ.
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C
f is everywhere continuous but not differentiable at x=(2n+1)π2,nZ
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D
f is continuous everywhere
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Solution

The correct option is D f is continuous everywhere
We have
f(x)=|sin x|We know that |x| and sinx are continuous everywhere.
Hence, |sin x| is continuous everywhere for all x.
|x| is non-differentiable at x=0.
Therefore, |sinx| is non-differentiable at x=0.
So, |sinx| is non-differentiable when sinx=0, or x=nπ,nZ.
Hence, f(x) is continuous everywhere but not differentiable at x=nπ,nZ


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