这道题怎么做呢

更新时间2019-01-05 21:54:18

lim(x→0)x^sinx

=e^ln[lim(x→0)x^sinx]

=e^lim(x→0)lnx^sinx

=e^lim(x→0)sinx*lnx

=e^lim(x→0)lnx/(1/sinx)

=e^lim(x→0)(1/x)/[-cosx/(sinx)^2]

=e^lim(x→0)(sinx)^2/(-x*cosx)

=e^0

=1

lim(x→0)x^sinx

=e^ln[lim(x→0)x^sinx]

=e^lim(x→0)lnx^sinx

=e^lim(x→0)sinx*lnx

=e^lim(x→0)lnx/(1/sinx)

=e^lim(x→0)(1/x)/[-cosx/(sinx)^2]

=e^lim(x→0)(sinx)^2/(-x*cosx)

=e^0

=1