Calculate Limit of 3/ (x (ln (x+4) - ln (x)) as x→∞

[intenzxboi]

Homework Statement

3/ (x (ln (x+4) - ln (x))

as x goes to infinity.

so first i look at this i i thought its going to 0 cause x is going to get larger at the bottom.

but then i see that the equation looks more like 3 / (x( ln ((x+1)/x))
ln ((x+1)/x) is going to 1. so that mean that ln 1= 0

so...
3 / x(0) = infinty?

 

[dx]

Nope, not infinity.

Hint: ln(a) - ln(b) = ln(a/b) and (1 + a/x)^x → e^a as x → ∞

 

[intenzxboi]

it doesn't go to zero?

 

[dx]

No. The limit is a positive number.