Question

大一高数证明题证明当x→0时,有：arctanx~x

Answer 1

令t=arctanx,则x=tant,x→0,则t→0,即,求证t→0时t=tant,tant=sint/cost,

tant/t=(sint/t)*(1/cost),t→0时,sint/t=1,1/cost=1,故,tant/t=1,得证.

所以t→0时t=tant,即,x→0时,有：arctanx~x