(1+2x)^(3/sinx)
=e^{[ln(1+2x)](3/sinx)}
∴lim(x→0)(1+2x)^(3/sinx)
=lim(x→0)e^{[ln(1+2x)](3/sinx)}
=lim(x→0)e^[2x(3/x)] (∵x→0时,2x是ln(1+2x)的等价无穷小量；x是sinx的等价无穷小量)
=e^6