计算lim(x趋于1)(x^x-1)/(xlnx)

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计算lim(x趋于1)(x^x-1)/(xlnx)
计算lim(x趋于1)(x^x-1)/(xlnx)

计算lim(x趋于1)(x^x-1)/(xlnx)
lim(x趋于1)(x^x-1)/(xlnx)
=lim(x^x-1)/(lnx^x)
=lim(x^x-1)/(ln(1+x^x-1)
=lim1/ln(1+x^x-1)^(1/(x^x-1))
=1/e

1

lim(x->1)(x^x-1)/(xlnx)
=lim(x->1) [e^(xlnx)-1]/(xlnx)
=lim(x->1) (xlnx)/(xlnx)
=1