Hi,

I was wondering if anyone had any thoughts on how to find examples of functions f(x) & g(x) which don't have limits for x -> 1 but do for which f(x) + g(x)?

Not sure where to start?

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- Oct 7th 2010, 04:43 PMinfinitepersepctiveshow to go about finding functions from limits?
Hi,

I was wondering if anyone had any thoughts on how to find examples of functions f(x) & g(x) which don't have limits for x -> 1 but do for which f(x) + g(x)?

Not sure where to start? - Oct 7th 2010, 05:15 PMChris L T521
- Oct 8th 2010, 01:08 AMinfinitepersepctives
Thanks Chris.

Is there a general rule I should follow... in your above example is looks like the denominator of g(x) is inverse to the denominator of f(x). Do you know if this is a general rule or is the answer to this question more of a brute force, try and see approach? - Oct 8th 2010, 05:24 AMHallsofIvy
No, Chris's whole point is that, just as there exist an

**infinite**number of pairs of numbers, x and y, such that x+ y= 4, so there exist an infinite number of pairs of functions, f and g, such that f(a)+ g(a) is equal to a given number or even such that $\displaystyle \lim_{x\to a} f(x)+ g(x)$ is equal to a given number. - Oct 10th 2010, 10:13 AMinfinitepersepctives
Trying to work through some problems without a book (it's on its way and should be here by Monday or Tuesday). Would the only functions that satisfy the above equation be ones where either f(x) or g(x) alone as x ->1 be where one or both of the f(x) or g(x) give a 0 as the denominator and where f(x) + g(x) don't give 0 as a denominator?