cosx=1-x^2/2!+x^4/4!+o(x^4)
e^x=1+x+x^2/2!+...
e^(-x^2/2)=1-x^2/2+(x^2/2)^2/2!+...
=1-x^2/2+(x^4)/8+o(x^4)
所以
原式=lim(1-x^2/2!+x^4/4!-(1-x^2/2+(x^4)/8))/x^4
=lim(x^4/24-x^4/8)/x^4
=1/24-1/8
=-1/12
cosx=1-x^2/2!+x^4/4!+o(x^4)
e^x=1+x+x^2/2!+...
e^(-x^2/2)=1-x^2/2+(x^2/2)^2/2!+...
=1-x^2/2+(x^4)/8+o(x^4)
所以
原式=lim(1-x^2/2!+x^4/4!-(1-x^2/2+(x^4)/8))/x^4
=lim(x^4/24-x^4/8)/x^4
=1/24-1/8
=-1/12