Continuity - Cal A  TOPIC_SOLVED

Limits, differentiation, related rates, integration, trig integrals, etc.

Continuity - Cal A

Postby nur123 on Sun Dec 30, 2012 12:09 am

Hello everyone!

I really need your help!

Please help with the following continuity problem -

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!
nur123
 
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Re: Continuity - Cal A  TOPIC_SOLVED

Postby nona.m.nona on Sun Dec 30, 2012 1:15 am

nur123 wrote: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?
nona.m.nona
 
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