Question

x的x次方的x次方在x趋进与0时求极限

Answer 1

lim(x->0)x^x
=lim(x->0)e^(xlnx)
=e^(lim(x->0)xlnx)
=e^(lim(x->0)lnx/(1/x))
(应用洛必达法则)
=e^(lim(x->0)(1/x)/(-1/x^2))
=e^(lim(x->0)(-x))
=e^0=1