What is L'Hopital's rule
L'Hopital (pronounced: Loh-pee-tahl OR Loh-pee-tall) allows us to evaluate limits that are in the forms:
We use L'Hopital's Rule to solve these limits, which tells us that we can differentiate both f(x) and g(x), then evaluate the limit through direct substitution. NOTE: in some cases, we have to do L'Hopital's rule several times before finally being able to evaluate the limit.
Practice problems
[source: BL]
Numerical problem
Evaluate the following limit.
Word problem
In the Cornucopia Bloodbath scene of Hunger Games, Francis Lawrence wanted to save filming time by having one camera pan around Jennifer Lawrence from behind from right to left, while another panned longer behind Josh Hutcherson (who stood to the left of her) from left to right, according to the equation below.
If Lawrence stood at an angle of the Cornucopia circle of 30˚ (π/3) and Hutcherson stood at an angle of 45˚ (root2/2), what is the limit that the second camera man can move before he collides with cameraman number one?
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