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)