limit problem

shanice12

New member
Joined
May 17, 2010
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3
my question is how to prove that the limit as x-->a [f(x)+g(x)] may exist even though the limit as x-->a of f(x) and the limit x-->a of g(x) do not exist

i cant seem to find an equation for f(x) or g(x) to satisfy the problem :|
 
If f and g are functions whose limits exist as x      a, then:\displaystyle If \ f \ and \ g \ are \ functions \ whose \ limits \ exist \ as \ x \ \implies \ a, \ then:

limxa(f+g)(x) = limxa[f(x)+g(x)] = limxaf(x) + limxag(x)\displaystyle \lim_{x\to a}(f+g)(x) \ = \ \lim_{x\to a}[f(x)+g(x)] \ = \ \lim_{x\to a}f(x) \ + \ \lim_{x\to a}g(x)

This should help.\displaystyle This \ should \ help.

f(x) = 1x and g(x) = 1x as x      0.\displaystyle f(x) \ = \ -\frac{1}{x} \ and \ g(x) \ = \ \frac{1}{x} \ as \ x \ \implies \ 0.

This should tell you that the converse may or may not be true.\displaystyle This \ should \ tell \ you \ that \ the \ converse \ may \ or \ may \ not \ be \ true.
 
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