Question

Find the indeterminate form and locate the limit using l'hopital's rule:
Find the limit as x approaches INFINITY at (ln(2x)-ln(x+1))

Answer 1

use log properties

Answer 2

log(a)-log(b)=log(a/b)

Answer 3

log(2x)-log(x+1)?

Answer 4

use the law I just mentioned

Answer 5

it works for any base

Answer 6

ln(2x)-ln(x+1)=?

Answer 7

also notifications aren't working too well for me

Answer 8

so log(2x)-log(x+1)=log2x/(x+1)

Answer 9

\[\ln(2x)-\ln(x+1)=\ln(\frac{2x}{x+1})\]

Answer 10

take the limit inside the the log there

Answer 11

what do you mean by take the limit inside the log?

Answer 12

\[\lim_{x \rightarrow \infty} \ln(\frac{2x}{x+1})=\ln(\lim_{x \rightarrow \infty} \frac{2x}{x+1})\]

Answer 13

so now i put in infinity for x?

Answer 14

yes but you get inf/inf and the directions wants you to find the limit using l'hospital and you can since you have inf/inf

Answer 15

so now take the derivative of the top and bottom

Answer 16

2

Answer 17

yes so you have ln(2) as the limit