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bjgawp
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Homework Statement
Prove that [tex]\lim_{x \to -\infty} \frac{2}{\sqrt{x^{4}+1}}=0\[/tex]
Homework Equations
The Attempt at a Solution
Preliminary Work
http://img339.imageshack.us/img339/401/proofzr7.jpg
Before proceeding on with the proof, when we look at the last line there seems to be a logical problem. We know that [tex]\epsilon[/tex] > 0 and x < N < 0 . Thus, it seems counter-intuitive that x is greater than a positive expression but less than a negative. Just a guess but I think it has something to deal with the second last line involving the square root. Thanks in advance!
Edit: Are there any texts that you guys suggest for learning epsilon-delta proofs? The examples that we do in class seem to be repetitive but when it becomes more abstract and general, some ingenuinity is needed and I would like to see some of these proofs worked out. Thanks!
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