西安毛子科技大学无穷小的比较XIDIAN UNIVERSITY(cosx-b)sinx=3,求a,b 的值.例4．设limx->0ex-a.: lim(e*-a)= 0,: lim(cosx-b)sinx = 0,解：+=a=1:: lim(e-a)=1-a=0lex_1~ x!x-0(cos x-b)sin x(cosx -b)sin x.. 3= lim-limete-1x-→0x-→0-a(cosx-b)sinx =lim(cosx-b)sinx=1-b=limx-0xx=b=-2无穷小的比较 例4. 设 求 的值. 0 (cos )sin lim 3, x x x b x → e a − = − a b, 解： 0 lim(cos )sin 0, x x b x → − = 0 lim( ) 0, x x e a →  − = 0 lim( ) 1 0 x x e a a →  − = − =  = a 1 0 0 (cos )sin (cos )sin lim lim 1 x x x b x x b x → → e a e − −  = − − 0 (cos )sin lim x x b x → x− = 1 x e x − 0 sin lim(cos ) x x x b → x = − = −1 b 3= = − b 2