|Nov1-09, 07:39 PM||#1|
2 functions f and g that dont have limits at a number c but fg and f+g do
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?
|Nov1-09, 08:06 PM||#2|
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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