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Exam 3 (Calculus II)

  1. Length of a Plane Curve Formula
    integral from a to b sqrt of 1+(dy/dx)^2 dx
  2. x= asinθ
    √a^2-u^2
  3. x= atanθ
    √a^2+u^2
  4. x= asecθ
    √u^2-a^2
  5. What does a formula like x^2+y^2=R^2 mean?
    that the segment is a circle with radius of 1
  6. How do you find work needed to move a full chain all at once?
    Use an integral from 0 to the length of the chain and then integrate the weight of the chain - the weight per foot of the chain *y
  7. How do you find the work needed to lift only part of a chain?
    To find the top half use an integral where it's the weight of the chain - the weight per foot *y. For the bottom it all moves the same so just multiply the length of the top part of the chain * the length of the bottom part of the chain * 2
  8. What is the unit for static force?
    lbs
  9. What is the unit for work?
    ft.-lbs.
  10. What do you need to check for when finding fluid force?
    if you need to multiply by 2 (triangles and circles)
  11. What do you use for L(y) for a cone?
    Πr^2 (Πx^2)
  12. What do you use for L(y) of a trough with isosceles ends?
    2x*length of the trough
  13. What do you use for L(y) of a trough with trapezoid ends?
    length of the trough*w*y (from slope)*(width of top +y)
  14. What do you use for L(y) for a cylinder (right circular tank)?
    Πr^2
  15. What do you use for L(y) for a hemispherical tank?
    Πr^2 (Πx^2)
  16. What do you use for L(y) for a trough with semicircle ends?
    2*x (found from sqrt of R^2-y^2)* length of the trough
  17. What do you use for L(y) for a semicircle?
    2*sqrt of R^2-y^2
  18. What do you use for L(y) for an isosceles triangle?
    2*what you get for x=...y
  19. What should you do if you have (x-2)^2 on the bottom below a number in partial fractions?
    integrate by moving the denominator to the top with a negative exponent
  20. derivative of secx
    sec(x)tan(x)
  21. secθ
    hypotenuse/adjacent
  22. sinθ
    opposite/hypotenuse
  23. tanθ
    opposite/adjacent
  24. integral of 1/[sqrt of a^2-f(x)^2] dx
    arcsin(f(x)/a)
  25. integral of 1/[a^2+f(x)^2]
    1/a arctan(f(x)/a)
  26. integral of 1/|f(x)|[sqrt of f(x)^2 - a^2] dx
    1/a arcsec(f(x)/a)
  27. e^0
    1
  28. ln(1)
    0
  29. What does 0 divided by something get you?
    0 (use during L'Hopital's questions)
  30. If nothing is in front of arctan and the parentheses have a fraction in them what does that mean?
    that the u value is a fraction
Author
gbiebs
ID
364958
Card Set
Exam 3 (Calculus II)
Description
Updated

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