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Calculus III (Assignment Problems) / Surface Integrals / Parametric Surfaces   [Notes] [Practice Problems] [Assignment Problems]

Calculus III - Assignment Problems
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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  

Calculus III (Assignment Problems) / Surface Integrals / Parametric Surfaces    [Notes] [Practice Problems] [Assignment Problems]

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