y=e^x y=e y轴

圆的一般方程x+y+Dx+Ey+F=0,则圆的标准方程为：(x-D/2)^2+(y-E/2)^2=D^2/4+E^2/4-F.则根据半径R>0可知：D^2/4+E^2/4-F>0.化简可得：D^2+E

x+y+Dx+Ey+F=0(x+D/2)+(y+E/2)=D/4+E/4-F=(D+E-4F)/4圆心(-D/2,-E/2)r=√(D+E-4F)/2与y轴切于原点所以圆心在x轴即-E/2=0E=0且

圆心(-d/2,-e/2)半径√[(d²+e²-4f)/4]与y轴切于原点所以圆心在x轴所以-e/2=0e=0圆心到y周距离等于半径|-d/2|=√[(d²+e²

E(X+2Y)^2=E(X^2+4XY+4Y^2)=E(X^2)+4E(XY)+4E(Y^2)=DX+(EX)^2+4EX*EY+4DY+(EY)^2=1+0^2+4*0*0+4*1+0^2=5

该题为隐函数求导.xy+e^(xy)=1则y+xy'+e^(xy)(y+xy')=0解得：y'=-y/x解答完毕.

根据圆得方程,计算D^2/4+E^2/4-F=（x+D/2)^2+（y+D/2)^2故上式成立

x²+y²+Dx+Ey+F=0可化为(x+D/2)²+(y+E/2)²+F-(D/2)²-(E/2)²=0圆心是（-D/2,-E/2）

x轴相切于原点可知点（0,0）是圆的方程的一点.带入可得F=0x²+y²+Dx+Ey+F=0可化为(x+D/2)²+(y+E/2)²+F-(D/2)²

X^2+Y^2+DX+EY+F=0(x+D/2)^2+(y+E/2)^2-D^2/4-E^2/4+f=0关于Y=2X对称则-E/2=2*(-D/2)即E=2D

这是个圆的方程(⊙o⊙)啊!x^2+y^2+Dx+Ey+F=0x^2+Dx+y^2+Ey+F=0x^2+Dx+D^2/4+y^2+Ey+E^2/4=(D^2+E^2-4F)/4(x+D/2)^2+(y

x²+y²+Dx+Ey+F=0(x+D/2)²+(y+E/2)²=D²/4+E²/4-F=(D²+E²-4F)/4圆心(

（1）圆心r²=D²/4+E²/4-F>0,把D²+E²=F²代入,得F²/4-F>0,解得F0）,F>4.（2）把圆心(-D/2

可解(ax+by+c)(dx+ey+f)展开为ad*x^2+(ae+bd)xy+be*y^2+(cd+af)x+(ce+bf)y+cf所以有ad=6ae+bd=-5be=-4cd+af=-11ce+b

E（XY）吧?就是X乘Y的期望如\y01x00.250.2510.250.25E(xy)=0*0*0.25+0*1*0.25+1*0*0.25+1*1*0.25=0.25

Cov(X,Y)=E(((X-E(X))(Y-E(Y)))根据协方差定义=E(xy-xE(y)-yE(x)+E(x)E(y))=E(xy)-E(x)E(y)-E(x)E(y)+E(x)E(y)=E(x

思路：x+y=e^xy,两边取微分d(x+y)=d(e^xy)dx+dy=e^xyd(xy)dx+dy=e^xy(xdy+ydx)dx+dy=xe^xydy+ye^xydx(xe^xy-1)dy=(1

两边求导得y'·e^y+(y+xy')/(xy)+e^(-x)=0

要注意E(kX)=kE(X),k是常数E[(X-E(X))*(Y-E(Y))]=E[XY-XE(Y)-YE(X)+E(X)E(Y)]=E(XY)-E(X)E(Y)-E(Y)E(X)+E(X)E(Y)=

在方程中令x=0可得，0＝lney(0)+1，从而可得，y（0）=e2将方程两边对x求导数，得：cos(xy)(y+xy′)＝1x+e−y′y将x=0，y（0）=e2代入，有e2＝1e−y′(0)e2

[e^(x+y)-e^x]dx+[e^(x+y)+e^y]dy=0(e^y-1)de^x+(e^x+1)de^y=0de^x/(e^x+1)+de^y/(e^y-1)=0dln(e^x+1)+dln(