Question

The value of `lim_(h→0)1/hint_2^(2+h)sin(x^2)dx`is?

The value of `lim_(h→0)1/hint_2^(2+h)sin(x^2)dx`is?

Answer 1

`lim_(h→0)(int_2^(2+h)sin(x^2)dx)/h`

This is `0/0` indeterminate so DLH's rule applies:

`= lim_(h→0)(d/(dh) int_2^(2+h)sin(x^2)dx)/(d/(dh)(h)`

Differentiating numerator using Liebnitz Rule:

`= lim_(h→0) sin(2+h)^2 *d/(dh)(2 + h)= sin 4`