Question

What's the Limit of x^(1/lnx) as x approaches zero from the right?

Answer 1

`e`

Explanation:

Since `x^y=exp(yln(x))` for all `x,y`, we can rewrite the expression as

`x^(frac(1)(ln(x)))=exp(frac(1)(ln(x))ln(x))=e`

Hence your function is just

`f:(0,infty)to RR : f(x)=e`

since it has constant value `e` in all the intervals `(0,epsilon)`, its limit on `0^+` is `e`