If `V=(x^2+y^2+z^2)^(-1/2)`, show that `x(delV)/(delx)+y(delV)/(dely)+z(delV)/(delz)=-V`

If u = (x^2+y^2+z^2)^(-1/2) then prove that (del^2u)/(delx^2)+(del^2u)/(dely^2)+(del^2u)/(delz^2) =0

If z (x + y) = x ^ (2) + y ^ (2) show that [(del z) / (del x) - (del z) / (del y)] ^ (2) = 4 [1 - (del z) / (del x) - (del z) / (del y)]

If 2^(x)=3^(y)=12^(z) show that (1)/(z)=(1)/(y)+(2)/(x)

If z=x+iy and |z-1|+|z+1|=4 show that 3x^(2)+4y^(2)=12

Show that the potential at a point of coordinates (x,y) with reference to the axis of the dipole as x -axis and the line perpendicular to the axis and passing through the centre of the dipole as y-axis is V = (1)/(4piepsi_(0)) , (px)/((x^(2) + y^(2))^(3//2)) and hence show that the components of the field along x- and y- axis are given by , E_(x) = (q)/(4pi epsi_(0)) , (2 x^(2) - y^(2))/((x^(2) + y^(2))^(5//2)) E_(y) = (p)/(4 pi epsi_(0)) , (3xy)/((x^(2) + y^(2))^(5//2)) [Hint : Find the value of cos theta and r in terms of x and y and substitute their values in the standard formula E_(x) = -(delV)/(delx) "and" E_(y) = -(delV)/(dely) ]

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= (4xyz)/((1-x^(2))(1-y^(2)) (1-z^(2)))

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= 4xyz/((1-x^(2))(1-y^(2)) (1-z^(2)))

if x^(2) + y^(2) =z^(2) , "then" 1/(log_(z+x)y) + 1/(log_(z-x)y) = _______

If V=x^(2)y+y^(2)z then find vec(E) at (x, y, z)

If a(y+z)=b(z+x)=c(x+y) then show that (a-b)/(x^(2)-y^(2))=(b-c)/(y^(2)-z^(2))=(c-a)/(z^(2)-x^(2))]