⑩天掌 Teaching Plan on Advanced Mathematics 两个重要极限 sInx (1)im-=1 x→>0y 证明设单位圆O,圆心角∠AOB=x,(0<x<3) 作单位圆的切线,得△CO 扇形OAB的圆心角为x, △OAB的高为BD, D 于是有sinx=BD,x=弧AB, tanx=AC, sInx sinx<x<tanx,即cosx< <Tianjin Polytechnic University Teaching Plan on Advanced Mathematics (1) 1 sin lim 0 = → x x x 证明 ) 2 , , (0  设单位圆 O 圆心角AOB = x  x  tan , sin , , x AC x BD x AB = 于是有 = = 弧 作单位圆的切线，得ACO. 扇形OAB的圆心角为x, OAB的高为BD, A C o B D sin x  x  tan x, 1, sin cos   x x 即 x 两个重要极限