Question

lim as x approaches 0+ (x^(-1/lnx))

Answer 1

lim(x->0+)(x^(-1/lnx))=L, if L exists. Then, take the ln of both sides
lim(x->0+)[ ln(x^(-1/lnx))]=lnL
lim(x->0+)[ (-1/lnx)(lnx)]=lnL
lim(x->0+)(-1)=lnL
-1=lnL
e^-1=L
1/e=L

Answer 2

You're a lifesaver-thank you!

Answer 3

No problem