Question

lim(x→0){[ln(1+(sinx)^2)-6*((2-cosx)^(1/3)-1)]/x^4} 用泰勒公式做

Answer 1

问题在这里,(2-cosx)^(1/3)=1+(1/6)x^2-(1/9*24)x^4+o(x^4)

x^4的系数错了

应该是(2-cosx)^(1/3)=(1-x^2/2+x^4/24+o(x^4))^(1/3)=1+(1/6)x^2-(1/24)x^4+o(x^4)