Originally Posted by

**christina182** Hi, thanx for the reply. I've done (a) with the epsilon-delta method (and I find that delta = epsilon establishes continuity).

In (b), we look at a situation where f(x) <=0.

The integral from

1

/

l f(x) dx

/

0

attains it's maximum at 1. And this is the case when f(x) = 1 and hence F(x) = x.

I guess that the integral attains it's min at -1. And this is the case when f(x) = -1 and hence F(x) = -x. I find it quite confusing that the maximum of I is the value of an integral, I mean, what is it that I should find - a value of x that min/max I or a function f (which is what I have done)?

Anyways, how do I show that the max/min I propose is actually max/min ... Can I do a proof by contradiction, if so, how do I get started?

In (c) I'm still lost... I mean, for

x<1: f_n(x) --> 0 for n --> infinity.

x=1: f_n(x)=1 --> 1 for n--> infinity.

And as {0,1} is a part of M i don't understand why we get into trouble at all :-)