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Paul
August 7, 2018

Calculus III - Practice Problems
 Applications of Partial Derivatives Previous Chapter Next Chapter Line Integrals Triple Integrals in Spherical Coordinates Previous Section Next Section Surface Area

## Change of Variables

For problems 1  3 compute the Jacobian of each transformation.

1.   [Solution]

2.   [Solution]

3.   [Solution]

4. If R is the region inside  determine the region we would get applying the transformation ,  to R. [Solution]

5. If R is the parallelogram with vertices , ,  and  determine the region we would get applying the transformation ,  to R. [Solution]

6. If R is the region bounded by , ,  and  determine the region we would get applying the transformation ,  to R. [Solution]

7. Evaluate  where R is the region bounded by , ,  and  using the transformation , . [Solution]

8. Evaluate  where R is the parallelogram with vertices , ,  and  using the transformation ,  to R. [Solution]

9. Evaluate  where R is the triangle with vertices ,  and  using the transformation ,  to R. [Solution]

10. Derive the transformation used in problem 8. [Solution]

11. Derive a transformation that will convert the triangle with vertices ,  and  into a right triangle with the right angle occurring at the origin of the uv system. [Solution]

Problem Pane
 Triple Integrals in Spherical Coordinates Previous Section Next Section Surface Area Applications of Partial Derivatives Previous Chapter Next Chapter Line Integrals

[Notes]

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