suppose that f and g are continious at (c,f(c)) and (c,g(c))
respectively then prove f/g is continious at c if g(c)!=0

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Request for Question Clarification by endo-ga on 04 Dec 2003 08:40 PST

Hi,

I'll start you off:
You need to start off with the definition of continuity, express it in
function of f and g, then show that the definition still holds for
f/g.

Hope this helps, if you need any more help please let me know.

Thanks.
endo

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Clarification of Question by maria2002-ga on 06 Dec 2003 19:57 PST

Please give me the answer in detail.

Hi,

We have by definition of continuity of f and g at c:

lim f(x) = f(c)
 x->c

and

lim g(x) = g(c)
 x->c

To prove continuity of f/g at c we express the definition of continuity:

lim (f/g)(x) = lim f(x)/g(x) = f(c)/g(c) = (f/g)(c)
 x->c            x->c

Q.E.D.

We have proven the continuity of f/g at c, if f and g are continuous
at c and if g(c)!=0.

I hope this answers your question, if you need any clarifications or
if something is unclear, please do not hesitate to ask.

Thanks.
endo