1. Use Stokes' Theorem to evaluate {image} {image} S is a part of the hemisphere {image} that lies inside the cylinder {image} oriented in the direction of the positive x - axis.
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Use Stokes' Theorem to evaluate {image} {image} C is the triangle with vertices (8, 0, 0); (0, 8, 0) and (0, 0, 10). C is oriented counterclockwise as viewed from above. Select the correct answer. The choices are rounded to the nearest hundredth.
-2,917.33
-2,919.33
-2,901.33
-4,437.33
-2,897.33
-2,893.33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. Use Stokes' Theorem to evaluate {image} {image} C the boundary of the part of the paraboloid {image} in the first octant. C is oriented counterclockwise as viewed from above.
{image} 1. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Use Stokes' Theorem to evaluate {image} where {image} C is the curve of intersection of the hyperbolic paraboloid {image} and the cylinder {image} oriented counterclockwise as viewed from above.
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. Calculate the work done by the force field {image} when a particle moves under its influence around the edge of the part of the sphere {image} that lies in the first octant, in a counterclockwise direction as viewed from above. Select the correct answer. The choices are rounded to the nearest hundredth.
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50