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

  1. 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?
     
  2. jcsd
  3. 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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