x趋向于0lim(sinx+f(x))/x^3=0求lim(tanx+f(x))/x^3

Question

x趋向于0 lim(sinx+f(x))/x^3=0求 lim(tanx+f(x))/x^3

Answer 1

移项得limf(x)/x^3=1+lim(sinx-x)/x^3 由于lim(sinx-x)/x^3当x趋于0时,分子分母都趋于0,根据洛必达法则对分子分母求导得 lim(sinx-x)/x^3=lim(cosx-1)/3x^2=lim(-sinx)/6x=lim(-cosx)/6=-1/6 代入后结果应为limf(x)/x^3=1+（-1/6)=5/6