# Trouble understanding!!

by sutupidmath
Tags: trouble
 P: 1,635 Well there is this theorem and i am having a little trouble understanding a part of it: -If the function u=g(x) has Uo as the limit at the limit point a (x-->a), but there exists some delta1 neighbourhood of a, such that for 0Uo), then the compound function y=f[g(x)] has b as the limit at the limit point a. That is: If lim(x-->a) g(x)=Uo ( u=g(x)=/=Uo for 0Uo)f(u)=b then lim(x-->a)f[g(x)]=b. The part that i do not fully understand, since i am not able to apply it on problems is the additional requirement on the first part of this theorem If the function u=g(x) has Uo as the limit at the limit point a (x-->a), but there exists some delta1 neighbourhood of a, such that for 0
 Sci Advisor P: 5,892 I can't fully grasp the point that is being made in the text. However, you could examine the implications of g(x) being a constant. It could be an example where f(Uo) is not b, i.e. there is some sort of singular point at Uo.
 P: 1,635 yeah i know that if this :but there exists some delta1 neighbourhood of a, such that for 0Uo)f(u)=b then since from the def, we would have for every epsylon there exists some delta such that whenever 0Uo)f(u)=b exists since it would not fullfile the requirement 0
P: 206

## Trouble understanding!!

I think the point of saying that such a neighborhood shouldn't exist is that it's possible for f(u) to be something like 1/(u - Uo). But if u(x) is identically Uo in a neighborhood of a, the limit can't exist. But I think if we assume that f(u) has at worst a removable singularity at Uo, then you don't need the assumption that such a neighborhood about a doesn't exist. But don't quote me on that.

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