Evaluate the volume between the surface z = 3 + 2x + xy, and the rectangle in the xy plane given by 0 < x < 2, 1< y< 3: Select one: O 12 O 27/2 O 45/2 O 28

Problem 1.19 Draw a circle in the xy plane. At a few representative points draw the vector v tangent to the circle, pointing in the clockwise direction. By comparing adjacent vectors, determine the sign of avx/ay and avy/ax. According to Eq. 1.41, then, what is the direction of V x v? Explain how this example illustrates the geo- metrical interpretation of the curl.

find u(x,y) , v(x,y) where f(z)=u+iv for function f(z)=Z2 e2z

Find the flux of F = xi - 2yj + zk across the portion of cylinder x² + z² = 9 in the first and forth octants. (3,-3,0) n X (0,0,3) (3,0,0) (0,3,0) y