Question

lim x -> 0^+ (1/x)^ xsquare

Answer 1

\[\lim_{x\to0^+}\left(\frac{1}{x}\right)^{x^2}~~?\]

Answer 2

yup ..

Answer 3

l'hospital rule too ~

Answer 4

LH rule for powers.. hmm.

Answer 5

\[\exp\left[\ln\left(\lim_{x\to0^+}\left(\frac{1}{x}\right)^{x^2}\right)\right]\]
Continuity of natural log as the argument approaches 0 from the right allows you to "pull out" the limit:
\[\exp\left[\lim_{x\to0^+}\ln\left(\frac{1}{x}\right)^{x^2}\right]\]
What do you know about logarithms when it comes to exponents like this one?