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Note: You are looking at a static copy of the former PineWiki site, used for class notes by James Aspnes from 2003 to 2012. Many mathematical formulas are broken, and there are likely to be other bugs as well. These will most likely not be fixed. You may be able to find more up-to-date versions of some of these notes at http://www.cs.yale.edu/homes/aspnes/#classes.
To compute the limit as n goes to infinity of f(n)/g(n), where f(n) and g(n) either both go to zero or both grow without limit, compute the limit as n goes to infinity of f'(n)/g'(n), where f'(n) and g'(n) are the derivatives of f(n) and g(n) with respect to n.
See http://www.karlscalculus.org/calc8_0.html for many worked examples.