Question

请问这两道题应该怎么做呢？

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Answer 1

第一题利用立方和公式，a^3+b^3=(a+b)(a^2-ab+b^2)
所以(x+(1-x^3)^(1/3))(x^2-(1-x^3)^(1/3)+(1-x^3)^(2/3))=x^3+1-x^3=1
于是x+(1-x^3)^(1/3)=1/[x^2-(1-x^3)^(1/3)+(1-x^3)^(2/3)].当x趋向于正无穷，分母也趋向于正无穷，故极限为0
第二题 直接取x无穷大，故a=0,b=6

Answer 2

(3)
y=1/x
y->0+
(1-y^3)^(1/3) = 1-(1/3)y +o(y)
1-(1-y^3)^(1/3) = (1/3)y +o(y)
lim(x->∞) [x+(1-x^3)^(1/3)]
=lim(y->0+) [1/y+(1-1/y^3)^(1/3)]
=lim(y->0+) [1+(y^3-1)^(1/3)] /y
=lim(y->0+) [1-(1-y^3)^(1/3)] /y
=lim(y->0+) (1/3)y /y
=1/3
(3)
lim(x->∞) (ax^3+bx^2+2x-1)/(3x^2 +2) =2
分母的阶数=2
=>分子的阶数=2
=> a=0
lim(x->∞) (ax^3+bx^2+2x-1)/(3x^2 +2) =2
lim(x->∞) ( bx^2+2x-1)/(3x^2 +2) =2
lim(x->∞) ( b+2/x-1/x^2)/(3+2/x^2) =2
b/3 =2
b=6
(a,b)=(2,6)

Answer 3

第一个题的答案是0
第二题的a=0 b=2

追答

写错了 b=6

Answer 4

啥题？…………看了个寂寞，照片呢？

追问

照片在问题下面 有一个图片的标志 点开即可