利用等价无穷小量代换lim(x─＞无穷)(3x-5)/(x＾3sin(1/x))

Question

利用等价无穷小量代换lim(x─＞无穷)(3x-5)/(x＾3sin(1/x))

Answer 1

原式=lim(x->∞)[(3x-5)/(x³(1/x-1/(6x³)+o(1/x³)))] (应用泰勒公式展开,o(x)表示高阶无穷小)=lim(x->∞)[(3/x-5/x²)/(1-1/(6x²)+o(1/x²))] =(0-0)/(1-0+0)=0