求极限，正确答案是-1/12，下图的解法为什么不对？ 10
2个回答
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x->0
分母
x^3.sinx = x^4 + o(x^4)
分子
cosx = 1- (1/2)x^2 + (1/24)x^4 +o(x^4)
e^(-x^2/2)
= 1 + [-(1/2)x^2] + (1/2)[-x^2/2]^2 +o(x^4)
=1 -(1/2)x^4 + (1/8)x^4 +o(x^4)
cosx - e^(-x^2/2) = -(1/12)x^4 +o(x^4)
lim(x->0) [cosx - e^(-x^2/2) ]/ (x^3.sinx)
=lim(x->0) -(1/12)x^4/ x^4
=-1/12
分母
x^3.sinx = x^4 + o(x^4)
分子
cosx = 1- (1/2)x^2 + (1/24)x^4 +o(x^4)
e^(-x^2/2)
= 1 + [-(1/2)x^2] + (1/2)[-x^2/2]^2 +o(x^4)
=1 -(1/2)x^4 + (1/8)x^4 +o(x^4)
cosx - e^(-x^2/2) = -(1/12)x^4 +o(x^4)
lim(x->0) [cosx - e^(-x^2/2) ]/ (x^3.sinx)
=lim(x->0) -(1/12)x^4/ x^4
=-1/12
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