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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?

  1. $\lim_{(a\to 0)} G(a)=1/2$
  2. $\lim_{(a\to0)} G(a)=1$
  3. $\lim_{(a\to 0)} G(a)=0$
  4. The limit $\lim_{(a\to 0)G(a)}$ does not exist.

I am completely stuck on it. How should I solve this?

4 Answers 4