求曲线y=(17-x²)/(4x-5)的渐近线
x→5/4时y→∞,故有垂直渐近线x=5/4；
x→∞时y→∞,因此无水平渐近线.
x→+∞lim(y/x)= x→+∞lim[(17-x²)/(4x²-5x)]=x→+∞lim[(17/x²-1]/[4-5/x]=-1/4
又 x→+∞lim[y+(x/4)]= x→+∞lim[(17-x²)/(4x-5)+(x/4)]
=x→+∞lim[4(17-x²)+x(4x-5)]/[4(4x-5)]=x→+∞lim(68-5x)/[4(4x-5)]
=x→+∞lim(68/x-5)/[4(4-5/x)]=-5/16
因此有斜渐近线y=-(1/4)x-5/16.