1.曲线y=x/(1-x^2)的渐近线有?2.ysinx+e^y-x=1确定y=y(x)的隐函数,则导数值y'(0)=

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1.曲线y=x/(1-x^2)的渐近线有?2.ysinx+e^y-x=1确定y=y(x)的隐函数,则导数值y''(0)=1.曲线y=x/(1-x^2)的渐近线有?2.ysinx+e^y-x=1确定y=y

1.曲线y=x/(1-x^2)的渐近线有?2.ysinx+e^y-x=1确定y=y(x)的隐函数,则导数值y'(0)=
1.曲线y=x/(1-x^2)的渐近线有?2.ysinx+e^y-x=1确定y=y(x)的隐函数,则导数值y'(0)=

1.曲线y=x/(1-x^2)的渐近线有?2.ysinx+e^y-x=1确定y=y(x)的隐函数,则导数值y'(0)=
1.曲线y=x/(1-x²)的渐近线有?
y=x/(1-x²)=x/(1+x)(1-x),因此有x=1和x=-1两条垂直渐近线;
又x➔∞limx/(1-x²)=0,故有一条水平渐近线y=0;
2.ysinx+e^y-x=1确定y=y(x)的隐函数,则导数值y'(0)=?
F(x,y)=ysinx+e^y-x-1=0
dy/dx=-(∂F/∂x)/(∂F∂y)=-(ycosx-1)/(sinx+e^y).(1);
将x=0代入原式得e^y=1,故有y=0;将(0,0)代入(1)式即得:y′(0)=1.

1.x=1,x=-1,y=0
2.y'(0)=0.5