## Continuity - Cal A

Limits, differentiation, related rates, integration, trig integrals, etc.
nur123
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Joined: Sat Dec 29, 2012 11:34 pm
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### Continuity - Cal A

Hello everyone!

I really need your help!

11. Given that lim[x->c](f(x)) and lim[x->c](g(x)) are both undefined:
a. Is it possible that lim[x->c](f(x)+g(x)) is defined? Give an example (graphically or algebraically)
b. Is it possible that lim[x->c](f(x)*g(x)) is defined? Give an example (graphically or algebraically)

Please explain in as much detail as possible!

Thanks A LOT!

nona.m.nona
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Joined: Sun Dec 14, 2008 11:07 pm
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### Re: Continuity - Cal A

11. Given that lim[x->c](f(x)) and lim[x->c](g(x)) are both undefined:
a. Is it possible that lim[x->c](f(x)+g(x)) is defined? Give an example (graphically or algebraically)
b. Is it possible that lim[x->c](f(x)*g(x)) is defined? Give an example (graphically or algebraically)
For (a), I would suggest thinking of functions which, in some sense, cancel out the undefined parts. For instance, 1/x is undefined at x = 0, as is -1/x. But what about their sum?