What is the value of lim_{x-0+} x^x ?

A. infty
B. 0
C. 1
D. Not defined

Question

What is the value of lim_{x->0+} x^x ?

A. infty
B. 0
C. 1
D. Not defined

Accepted Answer

1 x^x = e^(x*ln x) is a 0^0 indeterminate form. The key insight is to find the limit of the exponent x*ln(x) as x -> 0+. Even though ln(x) -> -inf, the factor x goes to 0 much faster, so x*ln(x) -> 0. Hence x^x = e^(x*ln x) -> e^0 = 1.

What is the value of lim_{x->0+} x^x ? A. infty B. 0 C. 1 D. Not defined