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Question

If f(x)=1 for x<0=1+sinx for 0x<π/2, then at x=0, then show that the derivative f(x) does not exist.

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Solution

We have f(0)=1+sin0=1.

RHL Rf(0)=limh01+sin(0+h)1h=limh0sinhh=1
and
LHL Lf(0)=limh011h=0
since value of RHL and LHL is not equal to the value of function at the point
Hence f(0) does not exist.

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