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Flashcards

Calc II Test 2

Brianna Lucido Calculus English 44 cards

Calc II Test 2

Cards in this deck (44)

  1. 1Basic formula for numeric integrationBasic formula for numeric integration
  2. 2Assumptions for numerical integrations- f(x) is continuous on [a,b]
    - n is a positive integer (and even for Simpson’s rule)
    [a,b] is divided into n sub intervals of length deltax, which equals (b-a)/n
  3. 3Midpoint rule formulaMidpoint rule formula
  4. 4Midpoint error formulaMidpoint error formula
  5. 5Trapezoidal rule formulaTrapezoidal rule formula
  6. 6Trapezoidal error formulaTrapezoidal error formula
  7. 7M for midpoint and trapezoidal error formulasMaximum value of |f’’(x)| on [a,b]
  8. 8Simpson’s rule formulaSimpson’s rule formula
  9. 9Simpson’s error formulaSimpson’s error formula
  10. 10M for Simpson’s error formulaMaximum value of |f’’’’(x)| on [a,b]
  11. 11When f(x) is continuous on [a,+oo)When f(x) is continuous on [a,+oo)
  12. 12When f(x) is continuous on (-oo,b]When f(x) is continuous on (-oo,b]
  13. 13If the limit exists, the improper integralconverges
  14. 14If the limit DNE the improper integraldiverges
  15. 15If f(x) is continuous over (-oo,+oo)If f(x) is continuous over (-oo,+oo)
  16. 16If f(x) is continuous over [a,b)If f(x) is continuous over [a,b)
  17. 17If f(x) is continuous over (a,b]If f(x) is continuous over (a,b]
  18. 18If f(x) is continuous on [a,b] except at cIf f(x) is continuous on [a,b] except at c
  19. 19Assumptions for comparison theorem of improper integrals- f(x) and g(x) are continuous over [a,+oo)
    - 0 < f(x) < g(x) for all x>a
  20. 20Comparison Theorem of Improper Integrals: If the integral of f(x) converges to +ooThe integral of g(x) converges to +oo
  21. 21Comparison Theorem of Improper Integrals: If the integral of g(x) converges to real number LThe integral of f(x) converges to real number M such that M < L
  22. 22Divergence testDivergence test
  23. 23Assumptions for integral test- f is continuous
    - f is decreasing
    - f(n) = a_n for all integers n > N
  24. 24Integral testIntegral test
  25. 25p-seriesp-series
  26. 26Assumptions for remainder estimate- f is continuous
    - f is decreasing
    - f(n) = a_n for all integers n > 1
  27. 27Remainder estimateRemainder estimate
  28. 28Cylindrical shell formula for rotating f(x) around y-axisCylindrical shell formula for rotating f(x) around y-axis
  29. 29Cylindrical shell formula for rotating g(y) around x-axisCylindrical shell formula for rotating g(y) around x-axis
  30. 30Trig substitution - a^2 - x^2- x=asin(theta)
    - identity: 1-sin^2=cos^2
  31. 31Trig substitution - a^2 + x^2- x=atan(theta)
    - identity: 1+tan^2=sec^2
  32. 32Trig substitution - x^2 - a^2- x=asec(theta)
    - identity: sec^2-1=tan^2
  33. 33Partial fraction decomposition when the degree of the numerator is greater than or equal to the degree of the denominatorlong division
  34. 34Partial fraction decomposition with nonrepeated linear factorsPartial fraction decomposition with nonrepeated linear factors
  35. 35Partial fraction decomposition with repeated linear factorsPartial fraction decomposition with repeated linear factors
  36. 36For each ax^2+bx+c, decomposition must include:For each ax^2+bx+c, decomposition must include:
  37. 37For each (ax^2+bx+c)^n, decomposition must include:For each (ax^2+bx+c)^n, decomposition must include:
  38. 38Arc length of a curveArc length of a curve
  39. 39Surface area of a solid of revolutionSurface area of a solid of revolution
  40. 40Derivative of a parametric curvey’(t)/x’(t)
  41. 41Second derivative of a parametric curveSecond derivative of a parametric curve
  42. 42Area under a parametric curveArea under a parametric curve
  43. 43Arc length of a parametric curveArc length of a parametric curve
  44. 44Surface area generated by a parametric curveSurface area generated by a parametric curve

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Calculus Flashcards on Calc II Test 2, created by Brianna Lucido on 05/03/2024.
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Brianna Lucido
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