([ varphi (x)] )^m+([ varphi (x)] )^n-([ varphi (x)] )^m (m,n为常数,且 gt mgt 0,-|||-[例27]试确定当 arrow 0 时,下列 __ 是关于x的三阶无穷小.-|||-A. sqrt [3]({x)^2}-sqrt [3](x) B. sqrt (1+{x)^3}-1 C. ^3+0.0002(x)^2 D. sqrt [3](sin {x)^3}-|||-解:根据三阶无穷小的定义,-|||-lim _(xarrow 0)dfrac (sqrt {1+{x)^3}-1}({x)^3}=lim _(xarrow 0)dfrac (dfrac {1)(2)(x)^3}({x)^3}=dfrac (1)(2) 因此,x→0时, sqrt (1+{x)^3}-1 是关于x的三阶无穷小.-|||-答案:B. ,与√2是等价无穷小 () .