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June 27th, 2010, 11:42 PM  #1 
Member Joined: Aug 2009 Posts: 69 Thanks: 0  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. 
June 28th, 2010, 04:59 AM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  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 . 
June 28th, 2010, 05:59 PM  #3 
Member Joined: Aug 2009 Posts: 69 Thanks: 0  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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