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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
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
追问
我那个是e^((x^x)/2)吧?
追答
你抄错了,不可能!
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