e^u=1+1/2u^2+1/6u^3+o(u^3)
sinx=x-1/3x^3+o(x^3)
e^sinx=1+sinx+1/2sinx^2+1/6sinx^3+o(sinx^3)
=1+[x-1/3x^3+o(x^3)]+1/2[x-1/3x^3+o(x^3)]^2+1/6[x-1/3x^3+o(x^3)]^3+o(x-1/3x^3+o(x^3))
將[x-1/3x^3+o(x^3)]^2,[x-1/3x^3+o(x^3)]^3,展開(kāi)時(shí),超過(guò)x^3的歸到o(x^3)
故寫(xiě)成了1/2[x+o(x^3)]^2,1/6[x+o(x^3)]^3+o(x^3)
e^sinx麥克勞林展開(kāi)到x^3
e^sinx麥克勞林展開(kāi)到x^3
答案說(shuō)e^x=1+1/2x^2+1/6x^3+o(x^3)
sinx=x-1/3x^3+o(x^3)
所以e^sinx=1+sinx=1/2sinx^2+1/6sinx^3+o(sinx^3)
=1+[x-1/6x^3+o(x^3)]+1/2[x+o(x^3)]^2+1/6[x+o(x^3)]^3+o(x^3) (*)
=1+x+1/2x^2+o(x^3)
請(qǐng)問(wèn)（*）式是如何得來(lái)的.
答案說(shuō)e^x=1+1/2x^2+1/6x^3+o(x^3)
sinx=x-1/3x^3+o(x^3)
所以e^sinx=1+sinx=1/2sinx^2+1/6sinx^3+o(sinx^3)
=1+[x-1/6x^3+o(x^3)]+1/2[x+o(x^3)]^2+1/6[x+o(x^3)]^3+o(x^3) (*)
=1+x+1/2x^2+o(x^3)
請(qǐng)問(wèn)（*）式是如何得來(lái)的.
數(shù)學(xué)人氣：881 ℃時(shí)間：2020-04-15 04:31:37
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