Question

Evaluate `lim_(xrarr0)x^(1/x)`?

Answer 1

I'm certain that the limit is `0`. (Graphing utiity.)
And I think.this reasoning is sound.

`ln x^(1/x) = 1/x lnx`

Which goes to `-oo` as `x rarr 0`

If `lnu rarr -oo`, then

`u = e^lnu rarr 0`