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bjgawp
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Homework Statement
I've got another question involving epsilon-delta proofs, one that is less concrete:
Prove that if g(x) [tex]\geq[/tex] 0 near c and [tex]\lim_{x \to c} g(x) = M [/tex] then M [tex]\geq[/tex] 0. Furthermore, if g(x) > 0 does it follow that M > 0?
Homework Equations
The Attempt at a Solution
Starting off with some preliminary work:
Let [tex]\epsilon[/tex] > 0. We must find [tex]\delta[/tex] > 0 such that |g(x) - M| < [tex]\epsilon[/tex] whenever 0 < |x - c| < [tex]\delta[/tex]
Does anyone have a hint they could provide? I'm not even sure how the end result of this proof is suppose to look like so that's a major set-back in proving this. Simpler, concrete examples require finding a [tex]\delta[/tex] in terms of [tex]\epsilon[/tex] but I don't know how that would apply here.