Calc 3 Exam 3

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  1. Area of a surface
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cint_%5E%5C%20%5C%20%5Cint_R%5E%5C%20%5Cmathrm%201dA&chs=140x56
  2. Average value of a function of two variables
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%7B%5Cint_%5E%5C%20%5C%20%5Cint_D%5E%5C%20%5Cmathrm%20f(x%2Cy)%20dA%20%7D%7B%5Cint_%5E%5C%20%5C%20%5Cint_D%5E%5C%20%5Cmathrm%201dA%20%7D&chs=190x112
  3. Jacobian for dV (rectangular)
    dx dy dz
  4. Volume of a solid
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cint_%5E%5C%20%5C%20%5Cint_%5E%5C%20%5C%20%5Cint_D%5E%5C%20%5Cmathrm%201dV&chs=210x96
  5. Average value of a function of three variables
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%7B%5Cint_%5E%5C%20%5C%20%5Cint_%5E%5C%20%5C%20%5Cint_D%5E%5C%20%5Cmathrm%20g(x%2Cy)dV%7D%7B%5Cint_%5E%5C%20%5C%20%5Cint_%5E%5C%20%5C%20%5Cint_D%5E%5C%20%5Cmathrm%201dV%7D&chs=222x112
  6. Convert the following to polar coordinates
    x
    y
    chart?chf=bg,s,00000000&cht=tx&chl=x%5E2%2By%5E2&chs=106x36
    • x=rcos(Θ)
    • y=rsin(Θ)
    • chart?chf=bg,s,00000000&cht=tx&chl=x%5E2%2By%5E2%3Dr%5E2&chs=180x36
  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
    • chart?chf=bg,s,00000000&cht=tx&chl=r%3D%5Csqrt%7Bx%5E2%2By%5E2%7D&chs=190x54
    • chart?chf=bg,s,00000000&cht=tx&chl=%5Ctheta%3Dtan%5E%7B-1%7D%5Cfrac%7By%7D%7Bx%7D%20(quadrants%20I%2CIV)&chs=432x58
    • chart?chf=bg,s,00000000&cht=tx&chl=%5Ctheta%3Dtan%5E%7B-1%7D%5Cfrac%7By%7D%7Bx%7D%2B%5Cpi%20(quadrantsII%2CIII)&chs=518x58
  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
    chart?chf=bg,s,00000000&cht=tx&chl=%5Crho%3D%5Csqrt%7Bx%5E2%2By%5E2%2Bz%5E2&chs=262x54

    • chart?chf=bg,s,00000000&cht=tx&chl=%5Cphi%3Dcos%5E%7B-1%7D%5Cfrac%7Bz%7D%7Bp%7D%20if%20%5Cphi%20%5B0%2C%5Cpi%5D&chs=298x58
    • chart?chf=bg,s,00000000&cht=tx&chl=%5Ctheta%3Dtan%5E%7B-1%7D%5Cfrac%7By%7D%7Bx%7D%20quadrants%20(I%2C%20IV)&chs=432x58
    • chart?chf=bg,s,00000000&cht=tx&chl=%5Ctheta%3D(tan%5E%7B-1%7D%5Cfrac%7By%7D%7Bx%7D%2B%5Cpi)%20quadrants%20(II%2C%20III)&chs=544x58
  13. What is the jacobian for dV in spherical coordinates
    chart?chf=bg,s,00000000&cht=tx&chl=dV%3D%5Crho%5E2sin%5Cphi%20d%5Crho%20d%5Cphi%20d%5Ctheta&chs=298x36
  14. What is the change of variables formula for double integrals?
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cint_%5E%5C%20%5C%20%5Cint_S%5E%5C%20%5Cmathrm%20f(x%2Cy)dxdy%3D%5Cint_%5E%5C%20%5C%20%5Cint_R%5E%5C%20%5Cmathrm%20f(u%2Cv)%20%7C%7BJ(u%2Cv)%5Cmid%20dudv&chs=644x56
  15. What is the change of variables formula for triple integrals?
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cint_%5E%5C%20%5C%20%5Cint_%5E%5C%20%5C%20%5Cint_D%5E%5C%20%5Cmathrm%20f(x%2Cy%2Cz)dV%3D%5Cint_%5E%5C%20%5C%20%5Cint_%5E%5C%20%5C%20%5Cint_R%5E%5C%20%5Cmathrm%20f(u%2Cv%2Cw)%5Cmid%20J(u%2Cv%2Cw)%5Cmid%20dudvdw&chs=814x56
Author:
stpierrewm
ID:
311414
Card Set:
Calc 3 Exam 3
Updated:
2015-11-15 03:37:54
Tags:
Calc Exam
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Calc 3 Exam 3
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Calc 3 Exam 3
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