Solving $\lim_{n\rightarrow \o}\frac{1}{x}^x$ Problem

[Physicsisfun2005]

Not sure if there is and answer

$$\lim_{n\rightarrow \o}\frac{1}{x}^x$$


i suck at latexing lol...liimit approaching zero from the right i think...and its (1/x)^x...the quantity to the x power.
...i don't think i can use l'hospital's rule...so how do i solve it?

 

[HallsofIvy]

(I assume it is x going to 0, not n!)

Sure you can use L'Hopital's rule. This is a (infinity)⁰ form so let y= (1/x)^x. ln(y)= x ln(1/x)= -xln(x) and you can write that as $-\frac{ln x}{\frac{1}{x}}$. Apply L'Hopital's rule to that. Whatever you get for ln y, the limit of the original problem is the exponential of that.

 

[Physicsisfun2005]

i got 1 as my answer...is that right?