Across
- 1. The expression for the evaluation of the indefinite integral of a positive function between two limits of integration.
- 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.
- 12. The number of square units needed to cover a surface.
- 15. An approximation of the definite integral.
- 18. The rate of change at a particular moment.
- 21. The amount of change divided by the time it takes.
- 22. The rate of change of velocity with respect to time.
- 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.
- 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.
- 27. The process of finding a derivative.
- 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.
- 29. The rate of change of the position of an object with respect to time.
- 30. A function that is defined by applying different formulas to different parts of its domain.
- 31. Zooming in at a point on the graph of a function until the function approaches the tangent line at that point.
- 36. In an application, maximizing or minimizing some aspect of the system being modeled.
- 37. An indefinite integral.
- 39. From A to B, a relation f such that every a A is uniquely associated with an object F(a) B.
- 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).
- 43. A rule which states that (uv)’ = uv’ + vu’
- 44. The third derivative.
- 45. A line which touches a point of a curve.
- 47. Has no end or goes on forever.
Down
- 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. A rule which states that (u/v)’ = (vu’-uv’) / v^2
- 4. The process by which an antiderivative is calculated.
- 5. A method of approximating to an integral as the limit of a sum of areas of trapezoids.
- 6. The local and global maximums and minimums of a function.
- 7. A method of approximating to an integral as a sum of quadratic terms.
- 8. The smallest value of a function for each value of the domain.
- 9. A method of finding the derivative of a composition of functions.
- 10. an integral without any specified limits, whose solution includes an undetermined constant C
- 11. A number or measurement that is close to or near its exact value.
- 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).
- 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.
- 15. A ratio that compares two quantities of different units.
- 16. A theorem that relates values of a function to a value of its derivative.
- 17. The set of all real numbers between two given numbers.
- 19. The ratio of change in the vertical axis to each unit change in the horizontal axis.
- 20. The process of evaluating an indefinite integral.
- 23. The highest value of a function for each value of the domain.
- 25. An integration method that essentially involves using the chain rule in reverse.
- 31. Approximating the value of a function by using the equation of the tangent line at a point close to the desired point.
- 32. Any ordered pair (x, y) where f’(x)=0 or is undefined.
- 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.
- 34. A point where a function changes concavity
- 35. The amount of space occupied in three dimensions and expressed in cubic units.
- 38. An equation that contains derivatives
- 40. A restriction on the range of the function
- 41. The absolute value or magnitude of velocity.
- 46. A line which passes through at least two points of a curve.