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Let f(x)=int0^g(x) dx/sqrt(1+t^2) where ...

Let `f(x)=int_0^g(x) dx/sqrt(1+t^2)` where `g(x) =int_0^cosx (1+sint^2) dt.` Also `h(x) =e^(-|x|)` and `l(x)=x^2 sin(1/x)` if `x != 0` and `l(0)` then `f'(pi/2)` equals

A

`l'(0)`

B

`h'(0^(-))`

C

`h'(0^(+))`

D

`underset (x rarr 0 )(lim) (1- cos x) /(x sin x)`

Text Solution

Verified by Experts

The correct Answer is:
C
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