# Homework Help: Delta-Epsilon Proof

1. May 18, 2012

### LaMantequilla

1. The problem statement, all variables and given/known data

Determine the limit l for the given a, and prove that it is the limit by showing how to find a ∂ such that |f(x)-l| < ε for all x satisfying o < |x-a| < ∂.

f(x) = x4 , arbitrary a

(Spivak's Calculus 5-3iv)

2. Relevant equations

3. The attempt at a solution

l = a4

The best I can do is show that |x2 - a2| < ε for |x-a|<∂1 = min(ε/(2|a|+1),1). After that, I get lost.

Since I found that |x2 - a2| < ε for |x-a|<∂1 = min(ε/(2|a|+1),1), can I rearrange |x4 - a4| to |(x2)2 - (a2)2| to find that ∂2=min(1,ε/(2|a|2+1)? This seems to be what Spivak's answer book is suggesting, but I'm not sure.

Can someone walk me through this? I'm pretty new to delta-epsilon proofs.

2. May 19, 2012

### Bacle2

Have you considered the factoring:

a2-b2=(a+b)(a-b)?

It may help.

And ,

I heard it goes great with butter.....

3. May 22, 2012

### Bacle2

Sorry if the last comment above seemed weird: I was just making reference to