- #1

MysticDude

Gold Member

- 142

- 0

[tex]\lim_{x \to +\infty} x^\frac{1}{x}[/tex]

I already know that the answer is one because [tex]\frac{1}{\infty}[/tex] is the same as 0 and anything to the zeroth power is 1. The thing that got me interested is about the fact that I practically substituted infinity into the problem to get the answer (sorry if I confuse you here). So the limit is practically [tex]\infty^\frac{1}{\infty}[/tex]. But I thought that that was indeterminate and what not. I also asked my

*very*intelligent teacher about this and he said "Well, we are approaching infinity, not actually reaching it." But then again, infinity is a concept and not a number.

I want to know what you think about this, and help me clear this up. Does this show that [tex]\infty^\frac{1}{\infty}[/tex] is not indeterminate or is it because of the limit that it is equal to 1. The infinity is the part that got me interested.

Well thanks for your any input that you may have. Just don't call me an idiot

**Sorry If This Is Confusing X(**