一道高数题:试确定A.B.C的值使得e^x(1+Bx+Cx^2)=1+Ax+o(x^3)

2025-03-26 12:47:38
推荐回答(2个)
回答1:

由于:e^x = 1 + x + x^2/2 + x^3/3! +o(x^3)
代入左边,有
左边=1 + (B+1)x + (C+B+1/2)x^2 + (C+B/2+1/6)x^3 + o(x^3)
所以有 B+1=A C+B+1/2=0 C+B/2+1/6=0
得: A = 1/3 B = -2/3 C = 1/6

回答2:

右式的Ax右面是零还是欧