# Homework Help: Prove if abs|f(x)| <= B for all x#0, then lim as x->0 of xf(x) = 0,

1. Oct 13, 2011

### anthonyg

1. if there is a number B such that abs|f(x)| <= B for all x#0, then lim as x->0 of xf(x) = 0,

2. Would I be able to get some help on how to prove this?

3. Given Epsilon > 0 such that delta = epsilon/B will prove the limit equals 0. (I know that may not make much sense but how am I supposed to make a solution when I don't know where to start... but I was warned so here is my attempt.) :|

Last edited: Oct 13, 2011
2. Oct 13, 2011

### SammyS

Staff Emeritus
Welcome to PF .

It looks like a fairly direct δ-ε proof.

What have you tried?

Where are you stuck?

3. Oct 13, 2011

### anthonyg

Thanks, the thing is I don't know where to start. I mean my teacher always starts out with given ε > 0 such that δ... I honestly just don't know where to go either.

4. Oct 13, 2011

### Staff: Mentor

I think your teacher starts out with a given ε > 0, and then figures out what δ needs to be.

Look at your text or class notes for some examples.

5. Oct 13, 2011

### anthonyg

Oh, yea, thanks! I didn't think of that! :surprised