lim(x趋向于无穷)x+sinx/x^2+1

Question

lim(x趋向于无穷)x+sinx/x^2+1

Answer 1

上下同除以x²,
x趋向于无穷,1/x趋向于0,1/x²也趋向于0
x趋向于无穷,sinx是周期函数,周期函数与无穷小数相乘为0
lim(x趋向于无穷)(1/x+sinx/x²)/(1+1/x²)=0/1=0