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## Homework Statement

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) = x

^{4}, arbitrary a

(Spivak's Calculus 5-3iv)

## Homework Equations

## The Attempt at a Solution

l = a

^{4}

The best I can do is show that |x

^{2}- a

^{2}| < ε for |x-a|<∂

_{1}= min(ε/(2|a|+1),1). After that, I get lost.

Since I found that |x

^{2}- a

^{2}| < ε for |x-a|<∂

_{1}= min(ε/(2|a|+1),1), can I rearrange |x

^{4}- a

^{4}| to |(x

^{2})

^{2}- (a

^{2})

^{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.