怎么求这个式子的高阶无穷小
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x->0
(1+2x)^(1/2)
= 1+ (1/2)(2x) -(1/8)(2x)^2 + o(x^2)
= 1+x - (1/2)x^2 +o(x^2)
(1+3x)^(1/3)
=1 + (1/3)(3x) -(1/9)(3x)^2 +o(x^2)
=1 + x -x^2 +o(x^2)
(1+2x)^(1/2) -(1+3x)^(1/3)
=[1+x - (1/2)x^2 +o(x^2)] -[1 + x -x^2 +o(x^2)]
= (1/2)x^2 +o(x^2)
(1+2x)^(1/2) -(1+3x)^(1/3) : 2价无穷小
(1+2x)^(1/2)
= 1+ (1/2)(2x) -(1/8)(2x)^2 + o(x^2)
= 1+x - (1/2)x^2 +o(x^2)
(1+3x)^(1/3)
=1 + (1/3)(3x) -(1/9)(3x)^2 +o(x^2)
=1 + x -x^2 +o(x^2)
(1+2x)^(1/2) -(1+3x)^(1/3)
=[1+x - (1/2)x^2 +o(x^2)] -[1 + x -x^2 +o(x^2)]
= (1/2)x^2 +o(x^2)
(1+2x)^(1/2) -(1+3x)^(1/3) : 2价无穷小
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