3. Consider a collection of intervals containing a point x0: fIjg fx0 aj ; x0...

3. Consider a collection of intervals containing a point x0: fIjg ¼ fðx0  aj ; x0 þ bjÞg, where fajg and fbjg are positive sequences which converge to 0. Prove that for a given function, f ðxÞ, with Mj and mj defined as in (10.2), that Mj  mj ! 0 if and only if f ðxÞ is continuous at x0.