credit Extra Problem #9 (4 pts) (a)
Due: 4/30
Let f(x,y) = 2y -6. Consider the rectangular region [0,3] by[0,4]. In what subregion of this rectangular region will the double integral of f(x,y) be maximum? Why? (b) What simple closed curve C gives the maximal value of the line integral (y^3-y)dx - 2x^3dy? (Hint: use Green's Theorem and the idea from part (a)). Extra credit Problem #10 (4 pts) (a) Due: 4/30
(b) (c) (d)
A river flows across the xy-plane in the positive x-direction and around circular a rock of radius 1 centered at the origin. The velocity of the river can be modeled using the potential function f(x,y) = x + (x / ( x2 + y2)). Compute the velocity vector field F = grad f(x,y). Show that div F = 0. Show that the flow of the river is tangent to the circle x2 + y2 = ...