Question

求极限lim x→0+(x的x次 方)

求极限lim x→0+(x的x次 方)

Answer 1

lim(x->0)x^x
=(x->0)e^{limxlnx}
=(x->0)e^{lim(lnx)/(1/x)} (用罗比达法则）
=(x->0)e^{lim(1/x)/(-1/x²)}
=(x->0)e^{lim(-x)}
=e^-0
=1/e^0
=1