lim (sinx-tanx)/sin(x³)
x→0
=lim x³(sinx-tanx)/x³sin(x³)
x→0
=lim (sinx-tanx)/x³
x→0
=lim sinx(1-secx)/x³
x→0
=lim (1-secx)/x²
x→0
=lim (cosx-1)/x²cosx
x→0
=lim (cosx-1)/x²
x→0
=-lim (1-cosx)/x²
x→0
=-lim 2sin²(x/2)/x²
x→0
=-lim ½sin²(x/2)/(x/2)²
x→0
=-½