求下列曲线的渐近线:(1) y=x^2/(x^2+2x-3) (2) y=(x^2-3x+2)/(1-x^2)

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/15 16:15:17

y=x²/(x²+2x-3)
limf(x)
=limx²/(x²+2x-3)
=limf(x)1/(1+2/x-3/x²)
=1
y=x²/(x²+2x-3)的水平渐近线为y=1
limf(x)
=limx²/(x²+2x-3)
当x²+2x-3=0即x0=-3或1时,limf(x)=∞
y=x²/(x²+2x-3)的铅直渐近线为x=-3和x=1
limf(x)/x
=limx²/x(x²+2x-3)
=limx/(x²+2x-3)
=lim(1/x)/(1+2/x-3/x²)
=0
y=x²/(x²+2x-3)没有斜渐近线
y=(x²-3x+2)/(1-x²)
limf(x)
=lim(x²-3x+2)/(1-x²)
=lim(1-3/x+2/x²)/(1/x²-1)
=-1
y=(x²-3x+2)/(1-x²)的水平渐近线为y=-1
limf(x)
=lim(x²-3x+2)/(1-x²)
当1-x²=0即x0=-1或1时,limf(x)=∞
y=(x²-3x+2)/(1-x²)的铅直渐近线为x=-1和x=1
limf(x)/x
=lim(x²-3x+2)/x(1-x²)
=lim(1/x-3/x²+2/x³)/(1/x²-1)
=0
y=(x²-3x+2)/(1-x²)没有斜渐近线
若limf(x)=a,则y=a为f(x)的水平渐近线
若limf(x)=∞,则x=x0为f(x)的铅直渐近线
若limf(x)/x=k、lim[f(x)-kx]=b,则y=kx+b为f(x)的斜渐近线

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