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Let f(x)={(1, AA, xlt0),(1+sinx, AA, 0le...

Let `f(x)={(1, AA, xlt0),(1+sinx, AA, 0lexlepi//2):}` then what is the value of `f'(x)` at `x=0`?

A

1

B

-1

C

`oo`

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
D
LHD `=lim_(hto0)(f(0-h)-f(0))/(-h)`
`=lim_(hto0)(1-1)/(-h)=0`
RHD `=lim_(hto0)(f(0+h)-f(0))/h`
`=lim_(hto0)(1+sin(0+h)-1)/h`
`=lim_(hto0)(sinh)/h=1`
`impliesLHD!=RHD`
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