The limit as x->0^+ (from above zero) of is 1, I know this from punching numbers into my calculator (and from Maple). My question is how can i show this algebraically?
For this problem you get a 0/0 case which is where L'Hopitals rule comes in (and since you are approaching it from the right and not the left you can use this: if you approached it from the left then it wouldn't exist altogether in the real numbers).
d/dx[ln(x+1)] = 1/(x+1) and d/dx(x) = 1. This will give a limit that can be evaluated.
If you are not familiar with L'Hopitals rule it is basically a rule that you can use if you get an indeterminate form like 0/0 or infinity/infinity type limits.