Calculus 2 exam 2

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Author:
AnnaRinaldo
ID:
224821
Filename:
Calculus 2 exam 2
Updated:
2013-06-24 12:10:04
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Calculus
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Description:
5.6 through 5.8
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  1. What is fluid force?
    The force "F" exerted by a fluid of constant weight density "w" against a submerged vertical plane region from y=c and d.

    F=wdc  h (y)×L (y) dy
  2. What is fluid force?
    The pressure on an object at a certain depth "h" in a fluid is p=wh where "w" is the weight density of the liquid per unit volume.
  3. What is Pascal's principle?
    The pressure exerted by a fluid at a depth "h" is transmitted equally in all directions.  P=f/a or force/area 
  4. What is the weight densities of water and sea water?
    Water=62.4   sea water=64.0
  5. Does the size of the body of water effect the fluid force?
    No.
  6. What is the moment of center of mass for one dimension?
    Let point masses be mlocated at x. The moment about the origin is M= m1x+ m2x+...+ mnxn. The center of mass is =M/m
  7. What is the center of mass for 2 dimensions?
    The point masses are mlocated at (x, y). The moment about the y-axis is m= +...+mn xn . The moment about the x-axis is mx= +...+my. The center of mass is (,) where =M/m and =M/m.
  8. What is the moment and center of mass of a planar lamina?
    f (x)  g (x), on [a, b]. The planar lamina of uniform density is "p" bounded by the graphs. 

    • moments about the x-axis 
    • M=p ab [f (x)+g (x)/2] × [f (x)-g (x)] dx
    • moments about the y-axis 
    • M=p a[f(x)-g(x)] dx

    • the center of mass 
    • () where y/m x/m    
    • where m= pa[f(x)-g(x)] dx is the mass of the lamina
  9. derivative of sinhu?
    coshu du/dx
  10. derivative of coshu?
    sinhu du/dx
  11. derivative of tanhu?
    sech2u du/dx
  12. anti-derivative of coshu?
    sinhu+c
  13. anti-derivative of sinhu?
    coshu+c
  14. anti-derivative of sech2u?
    tanhu+c
  15. hyperbolic sine?
    ex-e-x/2
  16. hyperbolic cosine?
    ex+e-x/2
  17. hyperbolic tangent?
    sinhx/coshx
  18. inverse hyperbolic sine?
    ln(x+(x2+1)1/2)
  19. inverse hyperbolic cosine?
    ln(x+(x2-1)1/2)
  20. inverse hyperbolic tangent?
    ln(1+x/1-x) / 2

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