anonymous 4 years ago limit as x approaches to zero....x power x power x

1. anonymous

0

2. anonymous

$\lim_{x \rightarrow 0} x^{x^{x}} = 0$ because $n^{0} = 1, so$ $0^{0} =1$ so $0^{0^{0}} = 0^1 = 0.$

3. dumbcow

No the limit is 1: limit of 0^0 is 1 1^0 = 1

4. anonymous

is thie answer 0 or 1?

5. dumbcow

its definitely 1 try plugging in x = .00001

6. anonymous

is that an indeterminate form?

7. dumbcow

0^0 ? yes it is, but the limit of x^x as x->0 is 1

8. anonymous

I'm still convinced it's 0 (see the attached plot). The limit of x^x for x->0 is 1, but for x^x^x, it should be 0.