Test 3MAT455

Name:Student ID:

Question 1

Show that is a conservative vector field, and find a function such

that .

Question 2

Use Green’s heorem is evaluate where , and C is the region

bounded by the lines x = 5, y = 0, and y = 35x.

Question 3

Given that , use Stokes’ Theorem to compute , where C is

the curve in which the cone intersects the plane , oriented the counterclockwiseviewed fromthe positive z-axis.

Question 4

If , use Divergence Theorem to evaluate where S is the surfacer

of the tetrahedron in the first octant.