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AP Calculus Ab

Subjects : math, ap, calculus
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. At c if lim f(x) as x approaches c exists but the limit is not equal to f(c)






2. 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






3. A point that represents the maximum value a function assumes over its domain






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






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






6. The limit of f as x approaches c from the right






7. If y=f(x) is continuous at every point of the close interval [a -b] and differentiable at every point of its interior (a -b) - then there is at least one point c in (a -b) at which f'(c)= [f(b)-f(a)]/(b-a)






8. If there is some number B that is greater than or equal to every number in the range of f






9. 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






10. 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






11. 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)






12. The smallest y-value of the function






13. The rate at which velocity changes over time; an object accelerates if its speed - direction - or both change






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






15. 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))






16. The value of the function at a critical point






17. Approximating the value of a function by using the equation of the tangent line at a point close to the desired point - L(x) = f(a) + f'(a)(x - a)






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






19. Has limits a & b - find antiderivative - F(b) - F(a) find area under the curve






20. Dividing an interval into n sub-intervals






21. The inverse of an eponential function






22. A function that can be graphed w/ a line or smooth curve






23. Decay: y=ab^x where a >0 and 0<b<1 - Growth: y=ab^x where a>0 and b>1






24. 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






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






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






27. Graph is symmetrical with respect to the origin; f(-x)=-f(x)






28. An equation involving two or more variables that are differentiable functions of time can be used to find an equation that relates the corresponding rates






29. 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






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






31. If there is some number b that is less than or equal to every number in the range of f






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






33. 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 right-most point of the sub-interval






34. Having the limits or boundaries established






35. 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






36. Intervals on which the second derivative is negative






37. The process of evaluating an indefinite integral






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






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






40. A surface or shape exposed by making a straight cut through something at right angles to the axis.






41. Input of function






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






43. 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






44. A procedure for finding the derivative of y with respect to x when the function relationship is defined implicitly






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






46. dy/dx






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






48. Zero of a function; a solution of the equation f(x)=0 is a zero of the function f or a root of the equation of an x-intercept of the graph






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






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