 NEWTON, Ask A Scientist! Name: Brian Status: student Age:  18
Location: N/A Country: N/A Date: N/A   My Calculus teacher made
up quiz off the top of his head for a section on L'Hopital's
Rule. The last question was to find the limit as x approaches
infinity in the equation cos(x)/ln(x). When you try to use
L'Hopital's you don't get an answer, yet when you graph the
equation, you see that it approaches 0. My teacher was not able
to explain why L'Hopital's rule falls flat on its face here. Can
you tell us how to solve the problem and why L'Hopital's rule
does not work?  L'Hospital's Rule does work in this case. All
the rule claims is that  lim f(x)/g(x) = lim f'(x)/g'(x)  which
is true. Unfortunately, this information doesn't help you find
the limit. To do that in this case, the best tool is common
sense: cos(x) is bounded; ln(x) is not.  This is a great lesson
whose relevance goes way beyond math. L'Hospital's rule is not
for finding limits. It's just a statement about functions and
their derivatives, and it