高等数学吧 关注：472,277贴子：3,882,377
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为什么这里xsinx展开后没有bx的四次？ bx^4 是不需要的项， 已经归纳于 o(x^3)
f(x)= x+aln(1+x)+bx.sinx
g(x)= kx^3
x->0
ln(1+x) = x-(1/2)x^2+(1/3)x^3 +o(x^3)
aln(1+x) = ax-(1/2)ax^2+(1/3)ax^3 +o(x^3)
sinx = x +o(x^2)
bx.sinx= bx^2 +o(x^3)
x+aln(1+x)+bx.sinx = (1+a)x +[-(1/2)a +b]x^2 + (1/3)ax^3 +o(x^3)
lim(x->0) [x+aln(1+x)+bx.sinx]/(kx^3) = 1
=>
1+a= 0 and -(1/2)a +b=0 and (1/3)a/k =1
a=-1 and b=1/2 and k=-1/3
f(x)= x+aln(1+x)+bx.sinx
g(x)= kx^3
x->0
ln(1+x) = x-(1/2)x^2+(1/3)x^3 +o(x^3)
aln(1+x) = ax-(1/2)ax^2+(1/3)ax^3 +o(x^3)
sinx = x +o(x^2)
bx.sinx= bx^2 +o(x^3)
x+aln(1+x)+bx.sinx = (1+a)x +[-(1/2)a +b]x^2 + (1/3)ax^3 +o(x^3)
lim(x->0) [x+aln(1+x)+bx.sinx]/(kx^3) = 1
=>
1+a= 0 and -(1/2)a +b=0 and (1/3)a/k =1
a=-1 and b=1/2 and k=-1/3
