Question

四求曲线 y=1/(x^2-4x-5) 的水平渐近线和铅直渐近线

Answer 1

lim[x→∞]1/(x^2-4x-5)=0
水平渐近线: y=0
lim[x→-1]1/(x^2-4x-5)=∞
lim[x→5]1/(x^2-4x-5)=∞
铅直渐近线:x=-1, x=5

Answer 2

解：因为lim(x趋向于∞)y=0，所以曲线的水平渐近线是直线y=0
又x=-1和x=5是y的无定义点，且lim(x趋向于-1)y=lim(x趋向于5)y=∞，所以曲线的铅直渐近线是直线x=-1和x=5