求下列函数的极值:
(1)y=x3-3x2+7 (2)
(3)(4)y=x2e-x
(5)(6)
(7)(8)
设个体域为实数集R,F(x):x>5,求下列0元谓词的真值.
(1)F(5). (2)F(). (3)F(-2). (4)F().
(5)F(). (6)F(7.9).
求下列二次曲面的中心:
(1)2xz+y2-2y-1=0;
(2)x2+y2+z2+2xy+6xz-2yz+2x-6y-2z=0;
(3)x2+y2+z2-4xy-4xz-4yz-3=0;
(4)5x2+9y2+9z2-12xy-6xz+12x-36z=0;
(5)4x2+y2+9z2-4xy+12xz-6yz+8x-4y+12z-5=0;
(6)x2+4y2+5z2+4xy-12x+6y-9=0;
(7)x2+25y2+9z2-10xy+6xz-30yz-2x-2y=0;
(8)2x2+5y2+2z2-2xy+4xz-2yz+14x-16y+14z+25=0.