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Paul
August 7, 2018

Calculus III - Assignment Problems
 Line Integrals Previous Chapter Surface Integrals (Introduction) Previous Section Next Section Surface Integrals

## Parametric Surfaces

For problems 1  10 write down a set of parametric equations for the given surface.

1. The plane containing the three points ,  and .

2. The portion of the plane  that lies in the 1st octant.

3. The portion of  that is behind

4. The portion of  that is in front of the xz-plane.

5. The cylinder .

6. The cylinder  for .

7. The sphere .

8. The portion of the sphere of radius 3 with  and .

9. The tangent plane to the surface given by the following parametric equation at the point .

10. The tangent plane to the surface given by the following parametric equation at the point .

11. Determine the surface area of the portion of  that is in the 1st octant.

12. Determine the surface area of the portion of  that is inside the cylinder .

13. Determine the surface area of the portion of  that is above the triangle in the xy-plane with vertices ,  and .

14. Determine the surface area of the portion of  that is in front of  with

15. Determine the surface area of the portion of  with ,  and  .

16. Determine the surface area of the portion of the surface given by the following parametric equation that lies above the triangle in the uv-plane with vertices ,  and .

17. Determine the surface area of the portion of the surface given by the following parametric equation that lies above the region in the uv-plane bounded by ,  and the u-axis.

18. Determine the surface area of the portion of the surface given by the following parametric equation that lies inside the cylinder .

 Surface Integrals (Introduction) Previous Section Next Section Surface Integrals Line Integrals Previous Chapter

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