Calc III Exam 1

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  1. Parametric equation of a line
    chart?chf=bg,s,00000000&cht=tx&chl=r(t)%3D%3Cx_o%2Cy_o%2Cz_o%3E%20%2B%20t%3Ca%2Cb%2Cc%3E&chs=436x44

    <point on line>+t<vector parallel to line>
  2. chart?chf=bg,s,00000000&cht=tx&chl=v%5Ccdot%5C%20v&chs=60x20
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cmid%5C%20v%20%5Cmid%5E2&chs=46x46
  3. chart?chf=bg,s,00000000&cht=tx&chl=(v%2Bw)%5Ccdot%20u&chs=138x38
    chart?chf=bg,s,00000000&cht=tx&chl=v%5Ccdot%20u%20%2Bw%5Ccdot%20u&chs=150x26
  4. chart?chf=bg,s,00000000&cht=tx&chl=proj_vU%3DU_%5Cparallel&chs=196x42
    chart?chf=bg,s,00000000&cht=tx&chl=(%5Cfrac%7Bu%5Ccdot%20v%7D%7Bv%5Ccdot%20v%7D)v&chs=98x52
  5. chart?chf=bg,s,00000000&cht=tx&chl=u_%5Cperp%20%3D&chs=76x28
    chart?chf=bg,s,00000000&cht=tx&chl=U-U_%5Cparallel&chs=100x38
  6. chart?chf=bg,s,00000000&cht=tx&chl=(u%2Bv)%5Ctimes%20w&chs=150x38
    chart?chf=bg,s,00000000&cht=tx&chl=u%5Ctimes%20w%20%2B%20v%5Ctimes%20w&chs=180x26
  7. If and  are the two sides of a parallelogram, what is the area of the parallelogram?
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cmid%20u%5Ctimes%20v%20%5Cmid&chs=82x40
  8. Equation of a plane (scalar equation and vector equation)
    • Vector Equation:
    • chart?chf=bg,s,00000000&cht=tx&chl=%3Cx-x_0%2Cy-y%2Bo%2Cz-z_0%3E%5Ccdot%20%5Cmathbf%7Bn%7D&chs=416x34
    • <x0,y0,z0> is a point on the plane, n is the normal vector to the plane

    • Scalar Equation: 
    • chart?chf=bg,s,00000000&cht=tx&chl=ax%2Bby%2Bcz%3Dd&chs=242x36
    • <a,b,c> is the normal vector to the plane
  9. chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%7Bd%7D%7Bdt%7D(%5Cmathbf%7Bu%7D(t)%5Ccdot%20%5Cmathbf%7Bv%7D(t))%3D&chs=240x68
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cmathbf%7Bu'%7D(t)%5Ccdot%5Cmathbf%7Bv%7D(t)%2B%5Cmathbf%7Bu%7D(t)%5Ccdot%5Cmathbf%7Bv'%7D(t)&chs=328x38
  10. chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%7Bd%7D%7Bdt%7D(%5Cmathbf%7Bu%7D(t)%5Ctimes%20%5Cmathbf%7Bv%7D(t))%3D&chs=252x68
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cmathbf%7Bu'%7D(t)%5Ctimes%5Cmathbf%7Bv%7D(t)%2B%5Cmathbf%7Bu%7D(t)%5Ctimes%5Cmathbf%7Bv'%7D(t)&chs=354x38
  11. arc length formula
    • Continuous on [a,t]
    • Traverses curve once on interval
    • chart?chf=bg,s,00000000&cht=tx&chl=%5Cint_a%5Et%20%5Cmathrm%5Cmid%20r'(u)%5Cmid%5C%2C%5Cmathrm%7Bd%7Du&chs=164x56
  12. chart?chf=bg,s,00000000&cht=tx&chl=%5Cmid%20r'(t)%5Cmid&chs=80x40
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%7Bds%7D%7Bdt%7D&chs=40x40 (derivative of arc length)
  13. Unit Tangent Vector T(t)
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%7Br'(t)%7D%7B%5Cmid%20r'(t)%5Cmid%7D&chs=66x86
  14. κ=curvature=
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cmid%5Cfrac%7Bd%5Cmathbf%7BT%7D%7D%7Bds%7D%5Cmid%20%3D%5Cfrac%7B1%7D%7B%5Cmid%5Cmathbf%7Bv%7D%5Cmid%7D%5Cmid%5Cfrac%7Bd%5Cmathbf%7BT%7D%7D%7Bdt%7D%5Cmid%20%3D%20%5Cfrac%7B%5Cmid%20%5Cmathbf%7Bv%7D%5Ctimes%20%5Cmathbf%7Ba%7D%5Cmid%7D%7B%5Cmid%5Cmathbf%7Bv%7D%5Cmid%5E3%7D&chs=294x90
  15. B=Unit Binormal Vector=
    TxN
  16. N=unit normal vector=
    • chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%7B%5Cmathbf%7BT'%7D%7D%7B%5Cmid%20%5Cmathbf%7BT'%7D%5Cmid%7D&chs=46x82 
    • or
    • chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%7B%5Cfrac%7Bd%5Cmathbf%7BT%7D%7D%7Bdt%7D%7D%7B%5Cmid%5Cfrac%7Bd%5Cmathbf%7BT%7D%7D%7Bdt%7D%5Cmid%7D&chs=54x126
  17. Components of acceleration 
    a=
    chart?chf=bg,s,00000000&cht=tx&chl=a%3Da_n%5Cmathbf%7BN%7D%2Ba_t%5Cmathbf%7BT%7D&chs=228x36
  18. chart?chf=bg,s,00000000&cht=tx&chl=a_n%3D&chs=70x26
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cmathbf%7Ba%5Ccdot%20n%7D%3D%5Cfrac%7B%5Cmid%20v%5Ctimes%20a%5Cmid%20%7D%7B%5Cmid%20v%5Cmid%7D&chs=176x86 or κchart?chf=bg,s,00000000&cht=tx&chl=%5Cmid%20v%5Cmid%5E2&chs=42x46
  19. chart?chf=bg,s,00000000&cht=tx&chl=a_t%3D&chs=64x28
    chart?chf=bg,s,00000000&cht=tx&chl=%5Cfrac%7Bd%5E2s%7D%7Bdt%5E2%7D%3D%5Cfrac%7B%5Cmathbf%7Ba%5Ccdot%20v%7D%7D%7B%5Cmid%20%5Cmathbf%7Bv%7D%20%5Cmid%7D&chs=146x82
Author:
stpierrewm
ID:
308200
Card Set:
Calc III Exam 1
Updated:
2015-09-20 18:57:27
Tags:
Calc III Exam
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Calc III Exam 1
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Calc III Exam 1
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