(x^3+3x^2)^(1\3)-(x^4-2x^3)^(1\4)=x[(1+3\x)^(1\3)-(1-2\x)^(1\4)] 1\x→0在0处泰勒公式有(1+x)^(1\m)=1+x\m+o(x)∴原式为x[(1+3\3x+o(1\x))-(1-2\4x+o(1\x))]=3\2+xo(1\x)∴极限为3\2