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Question

lf f(x)=sin1(sinx)x[6π,7π], then

A
f is continuous and differentiable everywhere
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B
f is differentiable at x=13π2
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C
f is not differentiable at x=13π2
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D
f is not continuous at x=13π2
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Solution

The correct option is C f is not differentiable at x=13π2
f(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪x6π;6πx<13π2π2;x=13π27πx;13π2<x7π
f(x)=⎪ ⎪⎪ ⎪1;6πx<13π21;13π2<x7π

For continuity,
Left hand limit f(c)= Right hand limit f(c+)=f(c)
f(13π2)=limh0(13π2h6π)=π2
f(13π2+)=limh0(7π13π2h)=π2
f(13π2+)=π2
f(x) is continuous in [6π,7π]
But clearly, f(x) is not differentiable at x=13π2
f(13π2)f(13π2+)


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