求 y=(-x^2 -2x)/(x - 1) 的渐近线
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求 y=(-x^2 -2x)/(x - 1) 的渐近线
求 y=(-x^2 -2x)/(x - 1) 的渐近线
求 y=(-x^2 -2x)/(x - 1) 的渐近线
因函数代数式分母不能是0,所以x=1是其其中一条渐近线(x→1-,y→+∞;x→1+,y→-∞});
lim{x→+∞}{-(x²+2x)/(x-1)}=-∞,lim{x→-∞}{-(x²+2x)/(x-1)}=∞
lim{x→∞}{[-(x²+2x)/(x-1)]/x}=lim{x→∞}{-(x+2)/(x-1)}=-1;所以另有渐近线斜率k=-1;
设x>1时渐近线方程为y=-x+a,因函数在此区域有极大值,故对任意x>1,-x+a>(-x^2-2x)/(x-1),
即 a>-3x/(x-1),不等式右端代数式的最大值是当x→+∞时极值-3,所以a=3,即渐近线为y=-(x+3);
当x
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