Find the area of the surface given by  z = f(x, y)that lies above the region R.   f(x, y) = 16 + 2x −3y R: square with vertices (0, 0), (8, 0), (0, 8), (8, 8)

Use the cross product to find the area of the portion of the plane defined by z = x + y which lies above the square [0, 1] x [0, 1] in the xy-plane. Draw a picture.

Calculate line integral p F.dr where F(x,y) (7x + y, 5x + 2y) and C is a rectangle with vertices (0, 2), (8, 2), (8, 5) and (0, 5) oriented clockwise.

The surface z = f(x, y) is shown in the diagram. The green point is A = (-2, 2, 0) and the red point is B = (2, 2, 0). Z 0,88 -0,25 -1,38 (a) Are the following quantities positive, negative, or zero? Positive v 1. fx (B) Negative v 2. fx(A) Negative v 3. fy(A) A 50 Positive v 4. fy(B) (b) Suppose a point P in the xy-plane moves in a straight line from the green point A to the red point B. Positive to negative v 1. Does the sign of fy(P) change from positive to negative, negative to positive, or is there no B change in sign? Negative to positive v 2. Does the sign of f, (P) change from positive to negative, negative to positive, or is there no change in sign?