|
|
![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Message
|
|
|
| ``Re: limit rule of compound function''
by azdbacks4234 on 2008-01-26 16:19:44 |
|
| I'm super busy with classes right now, but in the next week or so I might be able to add a proof, although I think it would be more beneficial to drop the assumption that g be continuous at $a$ and assume only that \lim_{x\rightarrow a}g(x) exists. In this case, we have
\lim_{x\rightarrow x_0}g(f(x))=\lim_{x\rightarrow a}g(x),
which implies the result as currently stated, since in this case
\lim_{x\rightarrow a}g(x)=g(a)=g(\lim_{x\rightarrow x_0}f(x)). Just a suggestion though. |
| | [ reply | up | top ] | |
|
|
|
|
|
|
|
