# Calculate the limit

## 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 gonna 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???

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dx
Homework Helper
Gold Member
Nope, not infinity.

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

it doesnt go to zero?

dx
Homework Helper
Gold Member
No. The limit is a positive number.

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