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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. 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. If f is continuous on [a -b] then at some point - c in [a -b] - f(c)= (1/(a-b))*?f(x)dx (with bounds a -b)






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






4. 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






5. The function that is integrated in an integral






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






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






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






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






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






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






12. A method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative.






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






14. A line that divides a figure in half so that each half is the mirror image of the other.






15. A method of representing the location of a point using an ordered pair of real numbers of the form (x -y)






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






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






18. Curve whose points are at a fixed normal distance of a given curve






19. The process of evaluating an indefinite integral






20. 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)






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






22. The inverse of an eponential function






23. Dividing an interval into n sub-intervals






24. A measure of how a function changes as its input changes.






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






26. Ratio between the length of an arc and its radius






27. 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






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






29. Intervals on which the second derivative is negative






30. The behavior of the graph of a function as x approaches positive infinity or negative infinity






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






32. The reciprocal of the sine function






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






35. A function whose dependent variable satisfies a polynomial relationship with one or more independent variables






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






37. Graph is symmetrical with respect to the y-axis; f(x) = f(-x)






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






39. A function that is a fixed numerical value for all elements of the domain of the function






40. 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






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






42. The smallest y-value of the function






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






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






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






46. If a function is on the closed interval [a - b] and F is an antiderivative (?) of f on [a -b] then ?f(x) dx from a to b is F(b) - F(a)






47. Intervals in which the second derivative is positive






48. A²=(b²+c²)-2(ab)Cos(A)






49. A point of discontinuity that is not removeable - it represents a break in the graph of f where you cant redefine f to make the graph continuous.






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







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