What Went Wrong in Evaluating the Limit Using L'Hospital's Rule?

[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?

 

[dacruick]

Can I see what you've done?

 

[lurflurf]

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?

 

[mathman]

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