# L'Hospital's Rule (products)

SpockTock
I came across the problem lim as x approaches infinity of xln((x+3)/(x)). This is an indeterminate limit so L'Hospitals rule must be used to evaluate it. I solved it to come out to negative infinity, but the graph says it's three. What did I do wrong in solving it?

## Answers and Replies

dacruick
Can I see what you've done?

Homework Helper
write
x log((x+3)/x)=3 [log(1+3/x)-log(1)]/(3/x)
then you won't need L'Hospital's Rule which would work despite being unneeded. As far as what the mistake was how would anyone know?

Science Advisor
You can also use the power series for ln: ln(1 + 3/x) = 3/x +O(1/x2)