AP Calculus AB Vocabulary

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Across
  1. 1. The expression for the evaluation of the indefinite integral of a positive function between two limits of integration.
  2. 3. A point or value of the independent variable at which the value of a function is not equal to its limit as the value of the independent variable approaches that point, or where it is not defined.
  3. 12. The number of square units needed to cover a surface.
  4. 15. An approximation of the definite integral.
  5. 18. The rate of change at a particular moment.
  6. 21. The amount of change divided by the time it takes.
  7. 22. The rate of change of velocity with respect to time.
  8. 24. A theorem that states if f is continuous on the closed interval [a, b] and k is any number between f(a) and f(b), then there is at least one number c in [a, b] such that f(c)=k.
  9. 26. The rate of change derived as the ratio of the differences between the initial and final values of the two quantities constituting the ratio.
  10. 27. The process of finding a derivative.
  11. 28. A rectangular sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the midpoint of the sub-interval.
  12. 29. The rate of change of the position of an object with respect to time.
  13. 30. A function that is defined by applying different formulas to different parts of its domain.
  14. 31. Zooming in at a point on the graph of a function until the function approaches the tangent line at that point.
  15. 36. In an application, maximizing or minimizing some aspect of the system being modeled.
  16. 37. An indefinite integral.
  17. 39. From A to B, a relation f such that every a A is uniquely associated with an object F(a) B.
  18. 42. A discontinuity c of the function f for which f(c) cannot be redefined so that the limit as x approaches c of f(x)=f(c).
  19. 43. A rule which states that (uv)’ = uv’ + vu’
  20. 44. The third derivative.
  21. 45. A line which touches a point of a curve.
  22. 47. Has no end or goes on forever.
Down
  1. 1. The limit of the ratio of the change in a function to the corresponding change in its independent variable as the latter change approaches zero.
  2. 2. A rule which states that (u/v)’ = (vu’-uv’) / v^2
  3. 4. The process by which an antiderivative is calculated.
  4. 5. A method of approximating to an integral as the limit of a sum of areas of trapezoids.
  5. 6. The local and global maximums and minimums of a function.
  6. 7. A method of approximating to an integral as a sum of quadratic terms.
  7. 8. The smallest value of a function for each value of the domain.
  8. 9. A method of finding the derivative of a composition of functions.
  9. 10. an integral without any specified limits, whose solution includes an undetermined constant C
  10. 11. A number or measurement that is close to or near its exact value.
  11. 13. A discontinuity c of the function f for which f(c) can be redefined so that the limit as x approaches c of f(x)=f(c).
  12. 14. A rectangular sum of the area under a curve where the domain is divided into sub-intervals and the height of each rectangle is the function value at the right endpoint of the subinterval.
  13. 15. A ratio that compares two quantities of different units.
  14. 16. A theorem that relates values of a function to a value of its derivative.
  15. 17. The set of all real numbers between two given numbers.
  16. 19. The ratio of change in the vertical axis to each unit change in the horizontal axis.
  17. 20. The process of evaluating an indefinite integral.
  18. 23. The highest value of a function for each value of the domain.
  19. 25. An integration method that essentially involves using the chain rule in reverse.
  20. 31. Approximating the value of a function by using the equation of the tangent line at a point close to the desired point.
  21. 32. Any ordered pair (x, y) where f’(x)=0 or is undefined.
  22. 33. A number to which the terms of a sequence get closer so that beyond a certain term, all terms are as close as desired to that number.
  23. 34. A point where a function changes concavity
  24. 35. The amount of space occupied in three dimensions and expressed in cubic units.
  25. 38. An equation that contains derivatives
  26. 40. A restriction on the range of the function
  27. 41. The absolute value or magnitude of velocity.
  28. 46. A line which passes through at least two points of a curve.