L'Hôpital's rules

Question 1

What cases does LH’s rule apply to? and what is it?

Answer 1

for 0/0 case and infinity/infinity case:

• lim f(x) approaches 0 or infinity
• lim g(x) appraches 0 or infinity

then:
lim f(x)/g(x) = lim f'(x)/g'(x)

Question 2

What Indeterminate functions can we apply LH’s rule?

Answer 2

Indeterminate products: 0 * infinity
Indeterminate differences: Infinity - infinity
Indeterminate Powers: 1^(infinity); 0^0; (infinity)^0

Rewrite to be a 0/0 case or infinity/infinity case:

Question 3

what can we do to simplify Indeterminate Powers?

Answer 3

take natural log of both sides to bring down the power