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The limit of x^x does equal one when approached from the right (i.e., when x is positive, reducing to zero). From the left, it also approaches one, but is only
by Xophmeister 12y ago
The limit of x^x does equal one when approached from the right (i.e., when x is positive, reducing to zero). From the left, it also approaches one, but is only continuous over the complex numbers. Anyway, while the limit approaches one from both sides, the function cannot be evaluated at x=0 and so is undefined.
- philh 12y agoWhy are you considering 0^0 to be the limit of the function x^x, rather than (say) 0^x or (e^(-1/x))^x?
- Grue3 12y agoJust because the function has different limits at some point does not mean it is undefined at that point. Consider the signum function. It has limit -1 when approached from negative side, limit 1 when approached from positive side, but is actually defined as 0 at zero.