∵a=lim(x->∞)[f(x)/x]
=lim(x->∞)[(2x³-x²+5)/(x(x²-2x+5))]
=lim(x->∞)[(2-1/x+5/x³)/(1-2/x+5/x²)]
=(2-0+0)/(1-0+0)
=2
b=lim(x->∞)[f(x)-ax]
=lim(x->∞)[(2x³-x²+5)/(x²-2x+5)-2x]
=lim(x->∞)[(3x²-10x+5)/(x²-2x+5)]
=lim(x->∞)[(3-10/x+5/x²)/(1-2/x+5/x²)]
=(3-0+0)/(1-0+0)
=3
∴y=2x+3(y=ax+b)是原函数的渐近线
∵lim(x->c+)f(x)≠∞,lim(x->c-)f(x)≠∞
∴没有垂直渐近线
故原函数只有唯一的一条渐近线y=2x+3.