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2 functions f and g that dont have limits at a number c but fg and f+g do 
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#1
Nov109, 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= lim_{x>c} f(x) and D = lim_{x>c} g(x) then the lim_{x>c} (f+g) = L + D and lim_{x>c} (fg) = LD but that's assuming both L and D exist. What if L and D don't exist? 


#2
Nov109, 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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