I don't see the different answers ... the limit is 1 for both x**x and x**0 as x -> 0 from above. 0**x goes undefined when x falls below 1, but that doesn't prove it stays undefined in the limiting case. So you get two answers agreeing on 1 and one failure to produce an answer out of the three cases. (misread as case of less than zero, as bart supposed, but ... )

Update: I should refine this to: any function from the set of all f(x,y) = g(x)**h(y) that converges on 0**0 will either get a 1 or be discontinuous only at the exact 0,0 point. I used to have to prove that kind of thing as homework, but that's going back nearly 30 yrs!