Calc

Across

4. approximating a function’s value at a point using the tangent line at a nearby point
8. the acronym for the theorem that states that for a continuous function f from a to b with value L between f(a) and f(b), there must be a value x=c such that f(c) = N.
9. growth, this process uses the formula: P = P0e^rt
10. a series is ___ convergent if it always converges
12. Acronym for the two theorems that relate derivatives and integrals with each other
15. this type of growth has a growth rate and carrying capacity
16. if f and g are continuous functions of t, the functions x = f(t) and y= g(t) are ___
18. differentiation, the process used to differentiate each side of an equation with two variables by treating one of the variables as a function of the other
19. type of definite integral that has at least one limit that approaches infinity
20. a method to find the volume of an object of revolution using the formula (R(x)2-r(x)2)dx
23. a finite ordered list of numbers
24. sum, an approximation of an integral by dividing it into summable sections
29. min, a point where the function’s derivative is 0 and changes from negative to positive
30. substitution, The process for integration by replacing a part of the function with a variable
31. the name of the type of error bound used to approximate the maximum error of a Taylor polynomial
32. a method to find the volume of an object of revolution by slicing it parallel to the axis of revolution
34. quantities that express both magnitude and direction
35. series, a function expressed as an infinite sum of its derivatives at a single point.
39. feature of a graph relating to the rate of change of a function’s derivative
42. the derivative of velocity
43. by parts, a method used to integrate functions that are products of two simpler functions
44. a method to find the volume of an object of revolution using the formula R(x)2dx
45. reduction, this method is used to rewrite expressions involving trigonometric terms with trigonometric terms of smaller powers
47. Rule, a rule that helps to find the limit of indeterminate forms
48. the equation for ___ is (dxdt)2+(dydt)2
49. an equation that relates a function and its derivatives.
50. two functions f and g are ___ if f(g((x)) = g(f(x))

Down

1. Rule, a rule that helps to find the derivative of composite functions
2. the process of finding maximum and minimum values given constraints
3. When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a ___
5. the distance between two points along a section of a curve
6. a series in which every other term is negative
7. the nth term test checks for ___
11. the p-series test checks for ___
13. a rule to find the derivative of two functions multiplied together
14. the function is ___ if you can find its derivative at all points
17. a series that increases/decreases by a constant factor
21. max, a point where the function’s derivative is 0 and changes from positive to negative
22. a taylor series centered around zero
25. Law of Cooling, This person’s law states that the rate of heat loss of an object is directly proportional to the difference in the temperatures between itself and its environment.
26. sections, the volume of an object of revolution is found using the sum of the areas of the ___ of the shape
27. fractions, the fractions used for the decomposition of a rational expression
28. rates, finding a rate of change of a quantity with respect to another quantity’s ROC
33. a function is ___ at a if the limit exists at a, the function is defined at a, and they have the same value
36. the slope of a line that is tangent to a specific function's curve
37. of change, the speed at which one quantity is changing with respect to another quantity
38. the value that a function approaches as the input approaches some value.
40. graphical representations of the solutions to a differential equation
41. a series is ___ convergent if it converges only sometimes
46. the derivative of position