Let $f$ be a continuous function on [$0, 1$] with $f(0) =1$. Let $ G(a) = 1/a ∫_0^af(x)\,dx$ then which of the followings are true?
- $\lim_{(a\to 0)} G(a)=1/2$
- $\lim_{(a\to0)} G(a)=1$
- $\lim_{(a\to 0)} G(a)=0$
- The limit $\lim_{(a\to 0)G(a)}$ does not exist.
I am completely stuck on it. How should I solve this?