# Thread: Calculus 2 limits as x-->0+

1. ## Calculus 2 limits as x-->0+

My teacher gave me this problem as an honors problem. She said that at one point I will have to use L'Hopitals rule to solve, but I have no idea where to start.

1. Evaluate the limit, if it exists.

l i m (x+1)^cotx
n-->0+

Any help would be greatly appreciated

2. Originally Posted by JubJub1991
My teacher gave me this problem as an honors problem. She said that at one point I will have to use L'Hopitals rule to solve, but I have no idea where to start.

1. Evaluate the limit, if it exists.

l i m (x+1)^cotx
n-->0+

Any help would be greatly appreciated
Let $f=x+1$ and $g=\cot x$.

We end up with a limit of the form $1^\infty$. To fix this notice $\displaystyle f^g = \exp\left(\frac{\ln f}{1/g}\right)$.

So $\displaystyle \lim_{x\to0}f^g = \exp\left(\lim_{x\to0}\frac{\ln f}{1/g}\right)$ and the limit is of the form $\displaystyle \frac00$ (can you see why?).

Now apply L'Hopital's rule.

3. I cannot thank you enough! I did not see that it was f raised to the g. My only other question is on the second line you have f^g= exp(ln f/(1/g)). What is the exp part?

4. $\exp(x) = e^x$