# Limits problem

• Feb 16th 2013, 02:04 PM
asilvester635
Limits problem
Ok tell me if I'm wrong for (k)
I got 1(0) = 0
• Feb 16th 2013, 02:08 PM
emakarov
Re: Limits problem
The answer is indeed 0, but for a different reason. This is the limit of composition g(f(x)), not of product g(x)f(x).
• Feb 16th 2013, 02:27 PM
asilvester635
Re: Limits problem
And (l) is undefined right?
• Feb 16th 2013, 03:03 PM
emakarov
Re: Limits problem
Quote:

Originally Posted by asilvester635
And (l) is undefined right?

Yes. Hopefully you can explain why.
• Feb 16th 2013, 03:06 PM
asilvester635
Re: Limits problem
Yes because it's undefined when x approaches -1 for f(x)
• Feb 16th 2013, 03:16 PM
emakarov
Re: Limits problem
Quote:

Originally Posted by asilvester635
Yes because it's undefined when x approaches -1 for f(x)

No, the behavior of f(x) near x = -1 is irrelevant to this question. What matters is the behavior of f(x) near x = 1. Moreover, it is not enough to say that $\displaystyle \lim_{x\to1}f(x)$ does not exist. If f(x) were 1 instead of 0, then $\displaystyle \lim_{x\to1}f(x)$ would still not exist, but $\displaystyle \lim_{x\to-1}f(g(x))$ would exist.