How do I show that x^x->1 as x->0?

[Treadstone 71]

How do I show that x^x->1 as x->0?

 

[shmoe]

Try using log's to convert the exponentiation into a product.

 

[Treadstone 71]

I can't find a lower bound for xlog(x).

 

[andrewchang]

use l'hopital's rule.

if you have lim x log x then x log x is the same as [log x / (1 / x)]

 

[Treadstone 71]

Got it. Thanks.

 

[shmoe]

You can also change it to what may be a more familiar limit by setting x=1/y.