Across
- 1. a rule that helps to find the limit of indeterminate forms
- 4. a series is ___ convergent if it converges only sometimes
- 6. the derivative of position
- 8. a rule to find the derivative of two functions multiplied together
- 11. two functions f and g are ___ if f(g((x)) = g(f(x))
- 12. the function is ___ if you can find its derivative at all points
- 13. the volume of an object of revolution is found using the sum of the areas of the ___ of the shape
- 14. The process for integration by replacing a part of the function with a variable
- 17. this type of growth has a growth rate and carrying capacity
- 22. a method used to integrate functions that are products of two simpler functions
- 23. the derivative of velocity
- 25. the distance between two points along a section of a curve
- 26. a series that increases/decreases by a constant factor
- 29. the speed at which one quantity is changing with respect to another quantity
- 32. a series in which every other term is negative
- 35. 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
- 38. the name of the type of error bound used to approximate the maximum error of a Taylor polynomial
- 40. graphical representations of the solutions to a differential equation
- 41. feature of a graph relating to the rate of change of a function’s derivative
- 43. a series is ___ convergent if it always converges
- 45. a method to find the volume of an object of revolution using the formula (R(x)2-r(x)2)dx
- 46. 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.
- 47. approximating a function’s value at a point using the tangent line at a nearby point
- 48. the p-series test checks for ___
- 49. an approximation of an integral by dividing it into summable sections
Down
- 2. growth this process uses the formula: P = P0e^rt
- 3. a finite ordered list of numbers
- 5. the slope of a line that is tangent to a specific function's curve
- 7. a function is ___ at a if the limit exists at a , the function is defined at a , and they have the same value
- 9. this method is used to rewrite expressions involving trigonometric terms with trigonometric terms of smaller powers
- 10. a method to find the volume of an object of revolution using the formula R(x)2dx
- 15. if f and g are continuous functions of t , the functions x = f(t) and y= g(t) are ___
- 16. a point where the function’s derivative is 0 and changes from positive to negative
- 18. the process of finding maximum and minimum values given constraints
- 19. the nth term test checks for ___
- 20. Acronym for the two theorems that relate derivatives and integrals with each other
- 21. When f '(x) changes from increasing to decreasing or decreasing to increasing , f(x) has a ___
- 24. an equation that relates a function and its derivatives.
- 27. a taylor series centered around zero
- 28. Rule a rule that helps to find the derivative of composite functions
- 30. the fractions used for the decomposition of a rational expression
- 31. quantities that express both magnitude and direction
- 33. 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.
- 34. the equation for ___ is (dxdt)2+(dydt)2
- 36. type of definite integral that has at least one limit that approaches infinity
- 37. a point where the function’s derivative is 0 and changes from negative to positive
- 39. finding a rate of change of a quantity with respect to another quantity’s ROC
- 40. a method to find the volume of an object of revolution by slicing it parallel to the axis of revolution
- 42. a function expressed as an infinite sum of its derivatives at a single point.
- 44. the value that a function approaches as the input approaches some value.