Question

一道微积分题目求解释

一道微积分题目求解释想知道我右边黑笔写的那个怎么推到答案的那个式子

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Answer 1

taylor展开算了.
e^x = 1 + x + x^2 / 2 + x^3 / 3!+ .
(1 + x + x^2 / 2 + o(x^2))(1+Bx+Cx^2)=1+Ax+o(x^2)
((1+Bx+Cx^2) + (x+Bx^2+o(x^2)) + (x^2 / 2 + o(x^2)) + o(x^2))=1+Ax+o(x^2)
1 + (1+B)x+(C+B+1/2)x^2 + o(x^2) = 1 + Ax + o(x^2)
1 + (1+B)x+(C+B+1/2)x^2 + o(x^2) = 1 + Ax + o(x^2)
= = 我忘了o(x^2)包不包括x^2了.
= = 好吧根据楼上的,不包括
A=1+B.