Calc II Exam 3

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Calc II Exam 3
2011-04-11 14:22:42
Calc II Exam

hydrostatic force, sequences and series
Show Answers:

  1. What is the formula for pressure in metric
    • P = pgd
    • Pressure = ro x gravity x depth
  2. What is the formula for Hydrostatic Force on an object
    • F=PA
    • Force = Pressure x Area
  3. Geometric series
    Exponant in the equation = n-1, full geometric series = ar^(n-1), if the absolute value of r is less then 1 then the series converges, if it is greater then one it diverges, converges to a/(1-r)
  4. P-Series
    1/(n^p), if p is less then 1 the series diverges, if it is greater it converges
  5. Divergence Test
    if the limit of the series does not = 0 then it diverges
  6. Convergence Test
    f must be continuous, positive and eventually decreasing, if the integral of f(x)dx converges, then the series converges, if it diverges, so does the series
  7. Compairison Test
    let the series An and Bn be two series that are always positive, if An is less then or equal to Bn and Bn conveges then An conveges, if An is larger then Bn and Bn diverges so does An
  8. Limit Compairison Test
    An and Bn have positive terms, if the lim of (An)/(Bn) is greater then 0 then they both converge or both diverge