I dont understand how to solve excercises of limit.
I know the answer is 0 but I dont know how this answer is derived.
1/0= undefined
How can I control if this answer is right ?
You have to pay attention to the fact that $\displaystyle {x\to+0}$ and not 0. Let's see what $\displaystyle {x\to+0}$ means. Yes, x is about zero, but a positive. It's like 0.00000000...00001, and 1/x=1,000,000,000...,000. A very large positive number, thus infinity.
So, $\displaystyle {2^{\frac {1}{x}}}$ is is going to be a very large number, infinity. Therfore, dividing a finit number by a very large one is going to give as 0.
Hope this helps!