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AP Calculus Ab

Subjects : math, ap, calculus
Instructions:
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. If f is continuous at x = a and lim f'(x) (from the left) = lim f'(x) (from the right) - then f is differentiable at x = a






2. The mathematical formulation corresponding to a continuous time model; an equation involving derivatives






3. Any value in the domain where either the function is not differentiable or its derivative is 0.






4. The value of the function approaches as x increases or decreases without bound






5. A function is locally linear at x = c if the graph fo the function looks more and more like the tangent to the graph as one zooms in on the point (c - f(c))






6. The integral of a rate of change is called the total change: ?(from a to b) F'(x)dx = F(b)-F(a) -find anti-derivatives






7. Amount of change / time it takes (amount of change/ length of interval)






8. sinA/a=sinB/b=sinC/c






9. A function F is called an __________ of a function f on a given open interval if F'(x) = f(x) for all x in the interval - Add + c at the end






10. The maximum distance that the particles of a wave's medium vibrate from their rest position






11. Series from n=0 to infinity of c_n(x-a)^n where a is it's center and c_n is a coefficient.






12. A²=(b²+c²)-2(ab)Cos(A)






13. Function e^x - where e is the number (approximately 2.718281828) such that the function e^x is its own derivative.






14. A function that is not algebraic; examples are: trigonometric - inverse trigonometric - exponential and logarithmic funtctions






15. Selection of a best element from some set of available alternatives.






16. The value that a function is approaching as x approaches a given value through values less than x






17. An approximation of the derivative of a function using a numerical algorithm numerical integration - an approximation of the integral of a function using a numerical algorithm oddfunction- f(-x)=-f(x)






18. A function f that gives the position f(t) of a body on a coordinate axis at time t






19. The process of evaluating an indefinite integral






20. If f(x) is continuous over [a -b] - then it has an absolute maximum and minimum value on [a -b].






21. Intervals in which the second derivative is positive






22. A limit in which f(x) increases or decreases without bound - as x approaches c






23. A function whose domain is divided into several parts and a different function rule is applied to each part






24. An integral without any specific limits - whose solution includes an undetermined constant c; antiderivative






25. Having the limits or boundaries established






26. (geometry)A curve generated by the intersection of a plane or circular cone






27. The local and global maximums and minimums of a function






28. d = v[( x2 - x1)² + (y2 - y1)²]






29. 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 left most point of the sub-interval






30. The function that is integrated in an integral






31. A determining or characteristic element; a factor that shapes the total outcome; a limit - boundary






32. Dividing an interval into n sub-intervals






33. If f'(c) = 0 and f''(c) > 0 then minimum; if f'(c) = 0 and f''(c) < 0 then maximum






34. A point where a function changes concavity; also - where the second derivative changes signs






35. Imaginary line drawn perpendicular to the surface of a mirror or any surface






36. logb mn = logbm + logb n - logb m/n = logb m - logb n - logb mn = n logb m - logb b = 1 - logb 1 = 0






37. Limit of an average velocity - as the time interval gets smaller and smaller. Let s (t) be the position of an object at time t. The instantaneous velocity at t = a is defined as lim(h goes to 0) [s(a+h)-s(a)] / h






38. When an absolute maximum or minimum occurs at the endpoint of the interval for which the function is defined






39. Either of the endpoints of an interval over which a definite integral is to be evaluated






40. If y is a function of x - y' = dy is the first order - or first - derivative of y with dx respect to x






41. Let f(x) be a function continuous on the closed interval [a -b]. If N is any real number between f(a) and f(b) - then there is at least one real number c between a and b such that f(c)=N






42. ex) dx - dy etc






43. A function that is continuous on both the left and right side at that point






44. An undetermined constant added to every result of integration (the added +c)






45. A straight line that is the limiting value of a curve






46. A variable occurring in a function - but on which the value of the function does not depend






47. T = ?X / 2 (yo + 2y1 + 2y2 ... + 2y + y) - A method of approximating to an intergral as the limit of a sum of areas of trapezoids. Can be done by averaging a left hand sum and a right hand sum






48. Any number that can be written in the form a + bi - where a and b are real numbers and i is the imaginary unit






49. When testing critical values - if the first derivative changes from negative to zero to positive - then that critical value is a local minimum of the function. If the first derivative changes from positive to zero of negative - then that critical val






50. A logarithm with the base e - written as ln