lim(x→0)x^sinx
=lim(x→0)e^[ln(x^sinx)]
=lim(x→0)e^(sinxlnx)
=e^[lim(x→0)sinxlnx]
=e^[lim(x→0)lnx/(1/sinx)]
=e^[lim(x→0)(1/x)/(-cosx/sin²x)]
=e^[lim(x→0)(-sin²x/xcosx)]
=e^[lim(x→0)(-2sinxcosx)/(cosx-xsinx)]
=e^0
=1