Question

微分中值定理 问题lim (cosx-(e^-1/2 (x^2))/ (x^4)) x→0怎么算

Answer 1

用泰勒公式：

cosx=1-x^2/2+x^4/4!+o(x^5)

e^(-1/(2x^2))=1-1/(2x^2)+[1/(2x^2)]^2/2+o(x^5)

所以：lim (cosx-(e^-1/2 (x^2))/ (x^4))

=lim(x^4/4!+(1/(2x^2))^2/2)/x^4

=1/24+1/8=1/6