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June 27th, 2010, 11:42 PM   #1
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proof of limits to infinity of rational functions?

basically, I've heard this all over the place:
lim n-> of f(n)/g(n) where f and g are polynomial functions = ...
0 if the degree of f is less than the degree of g or
positive or negative infinity if the degree of f is greater than the degree of g or
the ratio of the coefficients of the terms with largest exponents in f and g

but i've never seen a proof of that... and I really don't care to know something without knowing how to prove it, unless I am truly truly too far in over my head, which I'm not sure I am.
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June 28th, 2010, 04:59 AM   #2
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Re: proof of limits to infinity of rational functions?

If f and g are of the same degree, and x is not zero, then by dividing both top and bottom by x? you get:



and as x approaches infinity, both top and bottom approach finite limits, so the limit of f/g is .
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June 28th, 2010, 05:59 PM   #3
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Re: proof of limits to infinity of rational functions?

Ah! I see! cool!

and the proofs for the other two cases are simple enough. Thanks!
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