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2 functions f and g that dont have limits at a number c but fg and f+g do

by ibensous
Tags: functions, limits, number
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ibensous
#1
Nov1-09, 07:39 PM
P: 10
I was wondering if anyone knows of an example where f and g are two functions that do not have limits at the real number c but f+g and fg have limits at c.

I know that if f and g are functions and L= limx->c f(x) and D = limx->c g(x) then the limx->c (f+g) = L + D and limx->c (fg) = LD but that's assuming both L and D exist. What if L and D don't exist?
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l'H˘pital
#2
Nov1-09, 08:06 PM
P: 256
What if f = -g = 1/x?

lim x--> 0 of f or g is undefined, but lim x--> 0 f + g = 0

lim x--> 0 fg would be - infinity.


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