x的x次方的极限

Question

x的x次方的极限

Answer 1

问极限题要写清楚极限过程,x趋于多少?我估计是x→0+
lim[x→0+] x^x
=lim[x→0+] e^(xlnx)
=e^(lim[x→0+] xlnx)
=e^(lim[x→0+] lnx/(x^(-1)))
洛必达法则
=e^(lim[x→0+] -(1/x)/(x^(-2)))
=e^(lim[x→0+] -x)
=e^0
=1

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