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

1 Answer
May 10, 2018

#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#