Problem with limit

**totalnewbie** · December 6th 2006, 07:32 AM

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 ?

**ThePerfectHacker** · December 6th 2006, 07:47 AM

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 ?

Let us think about this.

What is,
$\lim_{x\to 0^+}2^{1/x}=?$
The function increases without bound.
Thus,
$\frac{1}{1+2^{1/x}}\to 0$
Because the denominator get larger and larger and larger.

**alinailiescu** · December 6th 2006, 08:45 AM

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.
Hope this helps!

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