Question

using L'hopital's rule evaluate the limit as x approaches infinity (1-(3/x))^(4x)

Answer 1

Start by writing

\(\displaystyle\left(1-\frac{3}{x}\right)^{4x}\) as \(\displaystyle \exp\left(4x\cdot\ln\left(1-\frac{3}{x}\right)\right)\)

Answer 2

ok i can get that far

Answer 3

\[\displaystyle \exp\left(4x\cdot\ln\left(1-\frac{3}{x}\right)\right)= \exp\left(\frac{\ln\left(1-\frac{3}{x}\right)}{\frac{1}{4x}}\right)\]

Answer 4

that's where i got stuck. i don't know what to do from there

Answer 5

use l'Hospitals on the stuff on the inside of exp

Answer 6

doesn't it equal 0/infinity?

Answer 7

l'hospitals rule doesn't work for those circumstances right?

Answer 8

0/0