Continuity - Cal A

[nur123]

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!

[nona.m.nona]

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?