西安毛子科技大学无穷小的比较XIDIANUNIVERSITS13sin x+ x? cosx例3计算 limx-0 (1+ cos x) ln(1 + x)解 x→0时, ln(1+x)～x,所以13sin x+x? cos -3sin x+ x? cosxxlim=limx→0x→0 (1+ cos x)ln(1+ x)(1 + cos x)x133sin x)lim= lim+lim x cos-2x→0x-0x→0 1+cosxxx无穷小的比较 例3 计算 2 0 1 3sin cos lim (1 cos )ln(1 ) x x x x → x x + + + 解 x → 0 时， ln(1 ) , + x x 所以 2 2 0 0 1 1 3sin cos 3sin cos lim lim (1 cos )ln(1 ) (1 cos ) x x x x x x x x → → x x x x + + = + + + 0 0 0 1 3sin 1 3 lim lim lim cos . x x x 1 cos 2 x x → → → x x x   =  + =   +  