Evaluate: limit as x approaches infinity ln(x^50)/x^100. State any theorems you used

Question

Evaluate: limit as x approaches infinity ln(x^50)/x^100.  State any theorems you used

anonymous · Answer

limit is 0
l'hopital's rule

anonymous · Answer

Yeah I know it is 0, I am just a little confused as how to get there

anonymous · Answer

bottom function grows faster than top function

anonymous · Answer

indeterminate form infinity over infinity
use L'H by taking the derivative of the top fuction and bottom fuction then take the limit.

anonymous · Answer

L'Hopital's Rule is basically just:

The derivative is the instantaneous rate of change. So if you have a bigger derivative, it means you're changing faster. Look at the derivative of the top and bottom. Don't you agree the bottom has a bigger derivative, and therefore will out grow the top?
So if the bottom out grows the top, then you're answers get smaller and smaller, so the limit is just 0