例1证明:当x→Q时,tanx-sinx为x的三阶无穷小 tanx- sin x 解∵lim x→0 1 sinx 1-cos x lim( x-0 cosx x limSⅧ 1-cosx 1 =lim x→0c0Sxx->0xx>0r 2 2 tanx-sinx为x的三阶无穷小例 1 证明:当x → 0时,tan x − sin x为x的三阶无穷小. 解 3 0 tan sin lim xx x x − →  ) sin 1 cos cos1 lim( 2 0 x x x x x x − =   → , 21 = tan x − sin x为x的三阶无穷小.2 0 0 0 1 cos lim sin lim cos1 lim x x x x x x x x − =   → → →