当x→0时,下列函数中哪些是x的高阶无穷小量?哪些是x的同阶无穷小量?哪些x的低阶无穷小量?

2个回答

  • 当x→0时,x的高阶无穷小量 1-cosx x^2 /2

    Limit [ (1-cosx) / x ,x->0] = Limit [ 2 sin(x/2)^2 / x ,x->0]

    = Limit [ 2 *(x/2)^2 / x ,x->0] = 0

    当x→0时,x的同阶无穷小量 x+tan2x 3x

    Limit [ (x + tan2x ) / x ,x->0] = Limit [ 3x / x,x->0] = 3

    当x→0时,x的等价无穷小量 2/πcosπ/2(1-x) = (2/π)sin(πx /2)

    Limit [ (2/π)sin(πx /2) / x ,x->0] = Limit [ x / x,x->0] = 1

    没有 x 的低阶无穷小量.