Accurate calculation method,

calculus

Example:

Consider the curve given by the square of y =2+xy.

(1) indicates that dy/dx = y/(2y-x).

(2) Find all the points (x, y) on the curve, where the slope of the curve is 1/2.

(3) The line that shows that no point (x, y) on the curve is tangent to the curve is horizontal.

(4) Let x and y be functions of time, which are expressed by the equation square = 2+xy. At time t = 5, the value of y is 3 and dy/dt = 6. Find the value of dx/dt at time t = 5.

Answer:

( 1)

The square of y =2+xy

2y(dy/dx) =x(dy/dx)+y( 1)

(2y-x)(dy/dx)=y

dy/dx = y/(2y-x)

(2)

When dy/dx = 1/2

y/(2y-x) = 1/2

2y=2y-x

x=0

The square of y =2+(0)y

y^2=2

Y=(+/-) root 2

(3)

Displayed when dy/dx = 0

have no answer

(4)

Prove that 2y*dy/dx=y+x*dy/dx.

So dy/dx=y/(2y-x)