lim sInx 1 lim sina(x (a(x)->0 x->0x 例1求lim tanx x-)0x r+ im tanx=lim Sinx 1 解1 lim Sinx.lim >0x x-0 x COSX x-0 x x-o coSx 例2求lim COSX x->0x 2Sm22 解 COSX m x->0x x->0x 2 2x-0x )2 SInA\2 = -lim 2 x->0 X 2 自贝 上页返回下页结束铃首页 上页 返回 下页 结束 铃 2 0 1 cos lim x x x − → = 2 2 0 2 2 0 ) 2 ( 2 sin lim 2 1 2 2sin lim x x x x x→ x→ = 1 sin lim 0 = → x x x  1 ( ) sin ( ) lim = x x a a (a(x)→0) 例 例 11 求 x x x tan lim →0  解 x x x tan lim →0 x x x x cos sin 1 lim 0 =  → 1 cos 1 lim sin lim 0 0 =  = → x → x x x x 解 解   x x x tan lim →0 x x x x cos sin 1 lim 0 =  → 1 cos 1 lim sin lim 0 0 =  = → x → x x x x 解  x x x tan lim →0 x x x x cos sin 1 lim 0 =  → 1 cos 1 lim sin lim 0 0 =  = → x → x x x x 解  x x x tan lim →0 x x x x cos sin 1 lim 0 =  → 1 cos 1 lim sin lim 0 0 =  = → x → x x x x  解 例 例 22 求 2 0 1 cos lim x x x − →  首页 2 1 1 2 1 2 2 sin lim 2 1 2 2 0 =  =         = → x x x  2 1 1 2 1 2 2 sin lim 2 1 2 2 0 =  =         = → x x x  2 0 1 cos lim x x x − → = 2 2 0 2 2 0 ) 2 ( 2 sin lim 2 1 2 2sin lim x x x x x→ x→ = 2 0 1 cos lim x x x − → = 2 2 0 2 2 0 ) 2 ( 2 sin lim 2 1 2 2sin lim x x x x x→ x→ =