求下列曲線的漸近線:(1) y=x^2/(x^2+2x-3) (2) y=(x^2-3x+2)/(1-x^2)
求下列曲線的漸近線:(1) y=x^2/(x^2+2x-3) (2) y=(x^2-3x+2)/(1-x^2)
優(yōu)質(zhì)解答
y=x²/(x²+2x-3)
lim
f(x)
=limx²/(x²+2x-3)
=limf(x)1/(1+2/x-3/x²)
=1
y=x²/(x²+2x-3)的水平漸近線為y=1
limf(x)
=limx²/(x²+2x-3)
當(dāng)x²+2x-3=0即x0=-3或1時,limf(x)=∞
y=x²/(x²+2x-3)的鉛直漸近線為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)沒有斜漸近線
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)的水平漸近線為y=-1
limf(x)
=lim(x²-3x+2)/(1-x²)
當(dāng)1-x²=0即x0=-1或1時,limf(x)=∞
y=(x²-3x+2)/(1-x²)的鉛直漸近線為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)沒有斜漸近線
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