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Summary: DRAFT VOL. 85, NO. 1, FEBRUARY 2012 1
Plausible and genuine extensions of
L'Hospital's Rule
J. Marshall Ash
DePaul University
Chicago, IL 60614
Allan Berele
DePaul University
Chicago, IL 60614
Stefan Catoiu
DePaul University
Chicago, IL 60614
A plausible extension
Roughly speaking, L'Hospital's Rule says that if f(x)/g(x) is indeterminate at infinity
and if x is large, then f(x)/g(x) is approximately equal to f (x)/g (x). Also, the
limit comparison test says that if an is approximately equal to bn then an converges
if and only if bn converges. The best thing that one could possibly hope for in trying
to combine these two observations is the equivalence
n=1
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