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AP Calculus

Nick Cento & Christina Capetola

See if you can master this puzzle!

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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.
Down
1.The theorem that establishes the connection between derivatives, antiderivatives, and definite integrals. The fundamental theorem of calculus is typically given in two parts.
2.A series which represents a function as a polynomial that goes on forever and has no highest power of x.
3.The distance between the center of a power series' interval of convergence and its endpoints.
4.Same as the derivative.
6.The process of finding the derivative of an explicit function. For example, the explicit function y = x2 – 7x + 1 has derivative y' = 2x – 7.
9.A model for growth of a quantity for which the rate of growth is directly proportional to the amount present. The equation for the model is A = A0bt (where b > 1 ) or A = A0ekt (where k is a positive number representing the rate of growth). In both formulas A0 is the original amount present at time t = 0.
11.The independent variable or variables in a set of parametric equations.
14.2.7182818284....
15.The total amount of space enclosed in a solid.
16.A function with a graph that moves downward as it is followed from left to right. For example, any line with a negative slope is decreasing.
18.The lowest point in a particular section of a graph.
20.A system of equations with more than one dependent variable. Often parametric equations are used to represent the position of a moving point.
22.A convergence test used when terms of a series contain factorials and/or nth powers.
23.A method for finding the derivative of a composition of functions. The formula is . Another form of the chain rule is .
25.A convergence test which compares the series under consideration to a known series. Essentially, the test determines whether a series is "better" than a "good" series or "worse" than a "bad" series. The "good" or "bad" series is often a p-series.
27.For a power series in one variable, the set of values of the variable for which the series converges. The interval of convergence may be as small as a single point or as large as the set of all real numbers.
28.An approximation of a function using terms from the function's Taylor series.
31.EX. Limit test for divergence,Alternating series test,Ratio test,
33.Distance covered per unit of time. Speed is a nonnegative scalar. For motion in one dimension, such as on a number line, speed is the absolute value of velocity.
34.EX. rationalizing substitutions,trig substitution,partial fractions
36.A convergence test often used when the terms of a series are rational functions. Essentially, the test determines whether a series is "about as good" as a "good" series or "about as bad" as a "bad" series. The "good" or "bad" series is often a p-series.
39.A function (or relation) written using (x, y) or (x, y, z) coordinates.
41.The power series in x – a for a function f . Note: If a = 0 the series is called a Maclaurin series.
46.A formula for the derivative of the quotient of two functions.
47.The process of finding an integral, either a definite integral or an indefinite integral.
51.The rate of change of the position of an object.

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