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Calculus and Beyond Homework Help
Limit on the edge of the domain
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[QUOTE="pasmith, post: 6863568, member: 415692"] You can't evaluate a function at points outside its domain. This is basic set theory. There are three quantifiers in the formal definition of [itex]\lim_{x \to a} f(x) = L[/itex]: [tex] (\forall \epsilon > 0)(\exists \delta > 0)(\forall x)(|x - a| < \delta \Rightarrow |f(x) - L| < \epsilon)).[/tex] The set over which [itex]x[/itex] is quantified must be some subset of the domain, or else we can't evaluate [itex]f(x)[/itex]. If you are given a domain which is an interval, then as far as you are concerned nothing outside of the closure of that interval exists. So the limit at an end point is necessarily the appropriate one-sided limit. [/QUOTE]
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Limit on the edge of the domain
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