Use the method of this example to calculate F · dr, C where F(x, y) = 2xyi + (y2 − x2)j (x2 + y2)2 and C is any positively oriented simple closed curve that encloses the origin.

Using Green's theorem we have:

int F.dr = int int d/dx ((y^2-x^2)/(x^2+y^2)^2) - d/dy (2xy/(x^2+y^2)^2) =

(2x^3 - 6xy^2) / (x^2+y^2)^3 - (2x^3 - 6xy^2) / (x^2+y^2)^3 = 0

Therefore:

int F.dr = 0

Step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line y = 120,000.

step-by-step explanation:

-10i^2-4i

step-by-step explanation:

evaluate for p=2,q=5i

(2−4)(2+5i)i

(2−4)(2+5i)i

=−10i2−4i