Across |

5. | The average height of the graph of a function. |

7. | A point at which the graph of a relation or function is not connected. |

8. | The highest point in a particular section of a graph. |

10. | An iterative process using derivatives that can often (but not always) be used to find zeros of a differentiable function. The basic idea is to start with an approximate guess for the zero, then use the formula below to turn that guess into a better approximation. This process is repeated until, after only a few steps, the approximation is extremely close to the actual value of the zero. |

12. | A theorem of calculus that ensures the existence of a critical point between any two points on a "nice" function that have the same y-value. |

13. | Describes a series that converges when all terms are replaced by their absolute values. To see if a series converges absolutely, replace any subtraction in the series with addition. If the new series converges, then the original series converges absolutely. |

17. | A major theorem of calculus that relates values of a function to a value of its derivative. Essentially the theorem states that for a "nice" function, there is a tangent line parallel to any secant line. |

19. | A graph or part of a graph which looks like a right-side up bowl or part of an right-side up bowl. |

21. | A class of problems in which rates of change are related by means of differentiation. Standard examples include water dripping from a cone-shaped tank and a man’s shadow lengthening as he walks away from a street lamp. |

24. | The process of writing any proper rational expression as a sum of proper rational expressions. This method is use in integration as shown below. |

26. | A method for finding the derivative of an implicitly defined function or relation. |

29. | A theorem that states the three alternatives for the way a power series may converge. |

30. | The value that a function or expression approaches as the domain variable(s) approach a specific value. |

32. | A discontinuity for which the graph steps or jumps from one connected piece of the graph to another. Formally, it is a discontinuity for which the limits from the left and right both exist but are not equal to each other. |

35. | definite integral for which the integrand has a discontinuity between the bounds of integration, or which has ∞ and/or –∞ as a bound. |

37. | A limit that has an infinite result (either ∞ or –∞ ), or a limit taken as the variable approaches ∞ (infinity) or –∞ (minus infinity). The limit can be one-sided. |

38. | A shape or solid which has an indentation or "cave". Formally, a geometric figure is concave if there is at least one line segment connecting interior points which passes outside of the figure. |

40. | A formula for the derivative of the product of two functions. |

42. | A hole in a graph. That is, a discontinuity that can be "repaired" by filling in a single point. |

43. | The x-value of a critical point. |

44. | The branch of mathematics dealing with limits, derivatives, definite integrals, indefinite integrals, and power series. |

45. | A curve that is smooth and contains no discontinuities or cusps. Formally, a curve is differentiable at all values of the domain variable(s) for which the derivative exists. |

48. | A model for a quantity that increases quickly at first and then more slowly as the quantity approaches an upper limit. This model is used for such phenomena as the increasing use of a new technology, spread of a disease, or saturation of a market (sales). |

49. | A number which is used to indicate the steepness of a curve at a particular point. The slope of a curve at a point is defined to be the slope of the tangent line.Thus it is found using the derivative. |

50. | The rate of change of velocity over time. |

52. | The result of taking the derivative of the derivative of the derivative etc. of a function a total of n times. |

53. | The product of a given integer and all smaller positive integers. |

54. | A function which gives the slope of a curve; that is, the slope of the line tangent to a function. (dy/dx) |

55. | A technique for finding the volume of a solid of revolution. This method is a specific case of volume by parallel cross-sections. |

56. | The formula for finding the derivative of a power of a variable. |

57. | A convergence test used for positive series which with decreasing terms. |

58. | A "number" which indicates a quantity, size, or magnitude that is larger than any real number. The number infinity is written as a sideways eight: ∞. Negative infinity is written –∞. |

59. | A convergence test used when series terms contain nth powers. |

60. | A line that touches a curve at a point without crossing over. Formally, it is a line which intersects a differentiable curve at a point where the slope of the curve equals the slope of the line. |