Anonymous

Hmmmm: will assume h ≡ x then the integral is G(x + 2) - G(2) where G ' exists ====> G is continuous ====> answer is 0 as x ---> 0

Anonymous

The limit has x approaching zero, but there is no x in the integral expression. The limit is simply the definite integral evaluated, and yes, of course the h makes a difference.

Anonymous

I suspect a typo. The integral does not have any x. So the limit as x tends to zero is just the definite integral. It is a complicated function of h.