" (ii) "x^(y)=y^(x)

x^(y)=y^(x),x=2y

If x^(y)=y^(x) then ((x)/(y))^((x)/(y))=x^((x)/(y)-k) where k=

If x^(y)=y^(x) show that (x/y)^(x/y)=x^((x)/(y)-1) if further x=2y then prove that y=2

the value of lim_(x rarr y)(x^(y)-y^(x))/(x^(x)-y^(y)) is:

If x ^(y) + y ^(x) = a ^(b) then show that (dy)/(dx) =- ((y x ^(y-1) + y^(x) log y)/( x ^(y) log x + x y ^(x -1)))

If x^(y)=y^(x) , prove that (dy)/(dx)=((y)/(x)-log y)/((x)/(y)-log x)

Sum of the series (x+y)(x-y) +1/(2!)(x+y) (x-y) (x^(2)+y^(2)) 1/(3!)(x+y)(x-y)(x^(4)+y^(4)+x^(2)y^(2))+... is

If x^(y) y^(x)=(x+ y)^(x+y).then (dy)/(dx)=

If x^y=y^x , then prove that (x/y)^(x/y)=(x)^((x)/(y)-1) .