(adsbygoogle = window.adsbygoogle || []).push({}); 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) = x^{4}, arbitrary a

(Spivak's Calculus 5-3iv)

2. Relevant equations

3. 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.

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# Homework Help: Delta-Epsilon Proof

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