Calc 3 Exam 3

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 Author: stpierrewm ID: 311414 Filename: Calc 3 Exam 3 Updated: 2015-11-14 22:37:54 Tags: Calc Exam Folders: Calc 3 Exam 3 Description: Calc 3 Exam 3 Show Answers:

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1. Area of a surface
2. Average value of a function of two variables
3. Jacobian for dV (rectangular)
dx dy dz
4. Volume of a solid
5. Average value of a function of three variables
6. Convert the following to polar coordinates
x
y
• x=rcos(Θ)
• y=rsin(Θ)
7. What is the jacobian for dA (polar)?
dA = r dr dθ
8. What is the jacobian for dV (cylindrical)?
dV = r dz dr dθ
9. Convert the following from rectangular to cylindrical coordinates
x
y
z
• x=rcosθ
• y=rsinθ
• z=z
10. Convert from cylindrical coordinates to rectangular coordinates
z
r
θ
• z=z
11. Convert from rectangular coordinates to spherical coordinates
x
y
z
• x=ρcosθsinφ
• y=ρsinθsinφ
• z=ρcosφ
12. Convert from spherical to rectangular coordinates
ρ
φ
θ

13. What is the jacobian for dV in spherical coordinates
14. What is the change of variables formula for double integrals?
15. What is the change of variables formula for triple integrals?

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