" (f) "quad x^(3)-x^(2)y+(1)/(3)xy^(2)-(1)/(27)y^(3)

Find the following products: (6x)/(5)(x^(3)+y^(3)) (ii) xy(x^(3)-y^(3))0.1y(0.1x^(5)+0.1y)( iv) (8)/(27)xyz((3)/(2)xyz^(2)-(9)/(4)xy^(2)z^(3))

1+8x^(3)+18xy-27y^(3)

27x^(3)+108x^(2)y+144xy^(2)+64y^(3)

The differential equation of all conics whose centre lies at origin, is given by (a) (3xy_(2)+x^(2)y_(3))(y-xy_(1))=3xy_(2)(y-xy_(1)-x^(2)y_(2)) (b) (3xy_(1)+x^(2)y_(2))(y_(1)-xy_(3))=3xy_(1)(y-xy_(2)-x^(2)y_(3)) ( c ) (3xy_(2)+x^(2)y_(3))(y_(1)-xy)=3xy_(1)(y-xy_(1)-x^(2)y_(2)) (d) None of these

The differential equation of all conics whose centre klies at origin, is given by (a) (3xy_(2)+x^(2)y_(3))(y-xy_(1))=3xy_(2)(y-xy_(1)-x^(2)y_(2)) (b) (3xy_(1)+x^(2)y_(2))(y_(1)-xy_(3))=3xy_(1)(y-xy_(2)-x^(2)y_(3)) ( c ) (3xy_(2)+x^(2)y_(3))(y_(1)-xy)=3xy_(1)(y-xy_(1)-x^(2)y_(2)) (d) None of these

The differential equation of all conics whose centre k lies at origin, is given by (a) (3xy_(2)+x^(2)y_(3))(y-xy_(1))=3xy_(2)(y-xy_(1)-x^(2)y_(2)) (b) (3xy_(1)+x^(2)y_(2))(y_(1)-xy_(3))=3xy_(1)(y-xy_(2)-x^(2)y_(3)) ( c ) (3xy_(2)+x^(2)y_(3))(y_(1)-xy)=3xy_(1)(y-xy_(1)-x^(2)y_(2)) (d) None of these

The differential equation of all conics whose centre klies at origin, is given by (a) (3xy_(2)+x^(2)y_(3))(y-xy_(1))=3xy_(2)(y-xy_(1)-x^(2)y_(2)) (b) (3xy_(1)+x^(2)y_(2))(y_(1)-xy_(3))=3xy_(1)(y-xy_(2)-x^(2)y_(3)) ( c ) (3xy_(2)+x^(2)y_(3))(y_(1)-xy)=3xy_(1)(y-xy_(1)-x^(2)y_(2)) (d) None of these

(x^(-3)-y^(-3))/(x^(-3)y^(-1)+(xy)^(-2)+y^(-3)x^(-1))=

If |x|<1 and |y|<1, find the sum of infinity of the following series: (x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+xy^(2)+y^(3))+

If x+y+z=xyz , prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/(1-3z^(2))= (3x-x^(3))/(1-3x^(2)).(3y-y^(3))/(1-3y^(2)).(3z-z^(3))/(1-3z^(2)) b) (x+y)/(1-xy) + (y+z)/(1-yz)+(z+x)/(1-zx)= (x+y)/(1-xy) .(y+z)/(1-yz).(z+x)/(1-zx)