If `x=1+y+y^(2)+…..` to `oo` then show that `y=(x-1)/(x)`

(i) If x = 3+ (3)/(y) + (3)/(y^(2)) + (3)/(y^(3)) + … + oo , then, show that y = (x)/(x-3) . (Where |y| lt 1 ). The following are the steps involv4ed in solving the above problem. Arrange them in sequential order. (A) xy - 3y =x (B) x=3 ((1)/(1-(1)/(y))) (C ) y(x-3)= x (D) x =3 ((y)/(y-1))

if x=1+y+y^(2)+............ to oo then y is equal to

If log (x^(2)+y^(2)) = 2 tan ^(-1) (x/y) " then show that " (dy)/(dx) = (y-x)/(y +x)

If x+y=e^(x-y) then show that (d^(2)y)/(dx^(2))=(4(x+y))/((1+x+y)^(3))

If y = x^(x ^(x^(x ^(x.... oo) then prove that x dy/dx = y^2/(1- y logx )

If log (x^(2)+y^(2))=tan^(-1)((y)/(x)), then show that (dy)/(dx)=(x+y)/(x-y)

If y = f(x) = (x+2)/(x-1) , x ne1 , then show that x = f(y) .

If y=x^(x^(x...oo)) then prove that xdy/dx=(y^2)/(1-ylogx)

If y=sqrt(x)+(1)/sqrt(x) , then show that 2x(dy)/(dx)+y=2sqrt(x) .