L'hospital and sketching curves

what is l'h rule

lim x->a f'(x)/g'(x)

when can L'H be applied

when the limit is 0/0, ∞/∞, 0*∞, or ∞-∞

how do you rewrite the form 0*∞ in order to use L'H

rewrite as 0/1/∞ or ∞/1/0 then apply L'H
- ususlaly put ln on top and polynomial on bottom

how do you rewrite the form ∞-∞ to be able to use L'H

rewrite the limit as a quotient by either finding a common denominator or factoring out a common factor

what do you need in order to sketch a curve

1. domain
2. intercepts (if y is too hard skip)
3. symmetry
4. asymptotes
5. determine where intervals are increasing or decreasing
6. local max/min
7. concavity and inflection points
8. graph it