Problem with limit

• December 6th 2006, 07:32 AM
totalnewbie
Problem with limit
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 ?
• December 6th 2006, 07:47 AM
ThePerfectHacker
Quote:

Originally Posted by totalnewbie
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 ?

$\lim_{x\to 0^+}2^{1/x}=?$
$\frac{1}{1+2^{1/x}}\to 0$
You have to pay attention to the fact that ${x\to+0}$ and not 0. Let's see what ${x\to+0}$ 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, ${2^{\frac {1}{x}}}$ 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.