y=(x-sinx)^(1/lnx)
两边同时取自然对数得：
lny=(1/lnx)·ln(x-sinx)=[ln(x-sinx)]/lnx
lim【x→0】lny
=lim【x→0】[ln(x-sinx)]/lnx
=lim【x→0】[1/(x-sinx)·(1-cosx)]/(1/x)
=lim【x→0】x(1-cosx)/(x-sinx)
=lim【x→0】(x³/2)/(x-sinx)
=lim【x→0】(3x²/2)/(1-cosx)
=lim【x→0】(3x²/2)/(x²/2)
=3
故lim【x→0】(x-sinx)^(1/lnx)=e^3