x-1例4 求 lim-1 x? -1消零因子x-1x-1解lim: lim.2-1大x-1 (x-1)(x +1)x-→111lim2x-1 x+1
例4 求 2 1 1 lim x 1 x x 解 2 1 1 lim x 1 x x 1 1 lim ( 1)( 1) x x x x 1 1 lim x x 1 1 . 2 0 ( ) 0 消零因子
sin x - cos x例5求lim元cos 2xx-4sin x -cos xsin x - cos x解limlimcos x- sin? x元cos 2x元x-x-44消零因子sin x - cos x: lim元(cos x - sin x)(cos x + sin x)x-4V2-1-1lim112元cos x + sin xx-4V2/2
例5 求 4 sin cos lim x cos 2 x x x 解 4 sin cos lim x cos 2 x x x 2 2 4 sin cos lim x cos sin x x x x 4 sin cos lim x (cos sin )(cos sin ) x x x x x x 4 1 lim x cos x sin x 1 1 1 2 2 2 . 2