Any, (a) (x + y) ০ (x - y) Show that, x + y x –y.

If y = x/(x+a) ,show that x dy/dx = y (1- y)

If log((x+y)/5) = 1/2 (log x + log y) , then show that x/y + y/x = 23 .

If y =6 (x +1) + (a+ b x) e ^(3x) then show that y" v + y = 4x + 8

If f (x, y) = 2x ^ (3) -11x ^ (2) y + 3y ^ (3), show that: x (delta f) / (delta x) + y (delta f) / (delta y ) = 3f (x, y)

If f (x, y) = 2x ^ (3) -11x ^ (2) y + 3y ^ (3), show that: x (delta f) / (delta x) + y (delta f) / (delta y ) = 3f (x, y)

If y =a cos x + (b + 2x) sin x then show that y" + y=4 cos x.

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) prop (x-y) , then show that (x^(3) +y^(3)) prop (x^(3)-y^(3)) .

Which one of the following is not a function? {(x , y): x , y in R , x^2=y} b. {(x , y): x , y in R , y^2=x} c. {(x , y): x , y in R , x=y^3} d. {(x , y): x , y in R , y=x^3}

Let f(x,y) = (y^(2) -xy)/(sqrt(x)-sqrt(y)) for (x,y) ne (0,0) . Show that lim_((x,y) to (0,0)) f(x,y) =0