z+1-x+2-y+2曲面

季亚复3595已知x,y,z满足1/2绝对值(x - y)+√(2y+z)+z^2 - z+1/4=0,求(x+y)^2的值 -
融洪翠13080441858 ______ 1/2绝对值(x-y)+√(2y+z)+z^2-z+1/4=01/2|x-y|+√(2y+z)+(z-1/2)^2=0 因为1/2|x-y|≥0,√(2y+z)≥0,(z-1/2)^2≥0 所以1/2|x-y|=0,√(2y+z)=0,(z-1/2)^2=0 x-y=0,2y+z=0,z-1/2=0 x=-1/4 y=-1/4 z=1/2(x+y)^2=(-1/4-1/4)^2=1/4

季亚复3595若x - 3=y - 2=z - 1,求x^+y^+z^ - xy - yz - xz的值,若x - 3=y - 2=z - 1,求x^+y^+z^ - xy - yz - xz的值 -
融洪翠13080441858 ______[答案] x-3=y-2 x-y=1 y-2=z-1 y-z=1 x-3=z-1 z-x=-2 x^2+y^2+z^2-xy-yz-xz =x(x-y)+y(y-z)+z(z-x) =x+y-2z x-3=z-1 y-2=z-1 2式相加,得 x+y-5=2z-2 x+y-2z=3 原式=3

季亚复3595将空间曲线一般方程转化为参数方程x^2+y^2+z^2=3,x+y+z=1 -
融洪翠13080441858 ______[答案] 把z=1-x-y带入到x^2+y^2+z^2=3得到x^2+y^2-x-y+xy=1配方为(2x+y-1)^2+3(y-1/3)^2=16/3令2x+y-1=4cost/√3 y-1/3=4sint/3联立后解得x=(2√3cost-2sint+1)/3y=(1+4sint)/3z=1-x-y=(1-2√3cost-2sint)/3所以x=(2√3cos...

季亚复3595计算曲面积分∫∫x^3dydz+y^3dzdx+z^3dxdy,∑是上半球面z=根下1 - x^2 - y^2的上侧 -
融洪翠13080441858 ______[答案] 在半球面∑上添加圆面S:(x²+y²=1,z=0),使之构成封闭曲面V=∑+S.∵∫∫x³dydz+y³dzdx+z³dxdy=0 (∵z=0,∴dz=0)∴ ∫∫x³dydz+y³dzdx+z³dxdy+∫∫x³dydz+y³dzdx+z...

季亚复3595(x+y+z)2 - (㎡x - y - z)2 -
融洪翠13080441858 ______ (x+y+z)2-(㎡x-y-z)2 分解因式:(x+y+z)2-(㎡x-y-z)2=(x+y+z-㎡x+y+z)(x+y+z+㎡x-y-z)=(x-㎡x+y+z+y+z)(x+㎡x+y+z-y-z)=(x-㎡x+2y+2z)(x+㎡x)=x(1+㎡)(x-㎡x+2y+2z)

季亚复3595x+y+z=3(1) x+2y+3z=6(2) 2x+y+2z=5(3) -
融洪翠13080441858 ______ x=3-y-z,从而3-y-z+2y+3z=3+y+2z=6 2x+y+2z=6-2y-2z+y+2z=6-y= 5 y=1; x=2-z 有3+y+2z=6得4+2z=6 z=1 从而x=1 即x=y=z=1

季亚复3595绝对值方程(|x+1|+|x - 2|)(|y+1|+|y - 2|)(|z - 3|+|z+1|)=36 求x+2y+3Z的最大、最小值 -
融洪翠13080441858 ______ (|x+1|+|x-2|) >= (|(x+1)-(x-2)|)=3 (|y+1|+|y-2|) >= (|(y+1)-(y-2)|)=3 (|z-3|+|z+1|) >= (|(z-3)-(z+1)|)=4 在满足上述条件的情况下,36只能分解为3x3x4 则必有 (|x+1|+|x-2|)=3,当-1<=x<=2时,此条件满足 (|y+1|+|y-2|)=3,当-1<=y<=2时,此条件满足 (|z-3|+|z+1|)=4,当-1<=z<=3时,此条件满足 则 最小值:x=y=z=-1,x+2y+3z = -6 最大值:x=y=2,z=3,x+2y+3z = 15

季亚复3595曲面积分 ∫∫(y^2 - x)dydz+(z^2 - y)dzdx+(x^2 - z)dxdy,∑为Z=1 - x^2 - y^2位于侧面上方的上侧 -
融洪翠13080441858 ______[答案] 楼上前一个积分算错了,这不是上半球面.我的答案: 如有不懂,

季亚复3595求教一道高数题 求曲面z=x^2+y^2+3在点M(1, - 1,5)处的切平面与曲面z=x^2+y^2+2x - 2y所围成的空间区域的体积 -
融洪翠13080441858 ______[答案] 曲面z=x^2+y^2+3在点M处的法向量 n=(2x,2y,-1)|M=(2,-2,-1) 写出切平面的方程 2(x-1)-2(y+1)-(z-5)=0 整理为 2x-2y-z+1=0 可以写成z=2x-2y+1 把平面和曲面z=x^2+y^2+2x-2y联立得到投影:x^2+y^2=1 所以体积 V=∫∫∫dxdydz=∫∫dxdy ∫(x^2+y^2+2x-2y-> 2x...