lim(arctan x-x)/sinx^3 x趨於0,能不能用等價無窮小的替換求解 答案是-1/3,用洛必達法則求的 另外我用等價無窮小的替換,結果為-1/6 =(sin x-x)/sinx^3 x趨於0 =(cosx-1)/[(cosx^3)*3x^2] x趨於0 =(-1/2)x^2/[(cosx^3)*3x^2] x趨於0 =(-1/2)/3cosx^3 x趨於0 =-1/6

lim(arctan x-x)/sinx^3 x趨於0,能不能用等價無窮小的替換求解 答案是-1/3,用洛必達法則求的 另外我用等價無窮小的替換,結果為-1/6 =(sin x-x)/sinx^3 x趨於0 =(cosx-1)/[(cosx^3)*3x^2] x趨於0 =(-1/2)x^2/[(cosx^3)*3x^2] x趨於0 =(-1/2)/3cosx^3 x趨於0 =-1/6

答案就是-1/6啊,用洛必達法則求也是這個結果
=(cosx-1)/(cosx^3)(3x^2)把x=0帶入cosx^3}
=-sinx/6x
=-1/6