Evaluate `lim_(y->0) [(sqrt(1-y^2)-sqrt(1+y^2))/y^2]`

int_0^1y^2sqrt(1-y^2)dy

lim_(yto0) (sqrt(1+sqrt(1+y^4))-sqrt2)/y^4

Evaluate (sqrt(x^2-y^2)+x)/(sqrt(x^2+y^2)+y) divide (sqrt(x^2+y^2)-y)/(x-sqrt(x^2-y^2))

Find the general solution of the differential equation x sqrt(1-y^(2))dx + y sqrt(1-x^(2)) dy =0.

Find the (dy)/(dx) of sqrt(1-x^2)+sqrt(1-y^2)=a(x-y)

Find the solution of the differential equation x sqrt(1+y^(2))dx+y sqrt(1+x^(2))dy=0

lim_(y to 0) ((y - 2) + 2sqrt(1 + y + y^(2)))/(2y) is equal to _______

The value of f(x,y)=((4sqrt(x^(3)y)-4sqrt(x^(3)))/(sqrt(y)-sqrt(x))+(1+sqrt(xy))/(4sqrt(xy)))^(-2)(1+2sqrt((y)/(x))+(y)/(x))^((1)/(2)) when x=9,y=0.04

Find the general solution of each of the following differential equations: x sqrt(1+y^(2))dx +y sqrt(1+x^(2))dy =0