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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. A logarithm with the base e - written as ln






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






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






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






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






7. dy/dx






8. 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






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






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






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






12. 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)






13. The mathematical process of obtaining the derivative of a function






14. The process of evaluating an indefinite integral






15. 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






16. 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.






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






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






19. The value of the function at a critical point






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






21. A basic definition in calculus f(x+h)-f(x)/h h doesn't equal 0






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






23. 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






24. Two curves that have perpendicular tangents at the point of tangency






25. 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






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






27. 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)






28. Input of function






29. Having the limits or boundaries established






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






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






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






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






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






35. 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)






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






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






38. 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






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






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






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






42. The smallest y-value of the function






43. 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






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






45. If f(x) is differentiable over (a -b) and continuous on [a -b] and f(a) = f(b) - then there exists c on (a -b) such that f'(c) = 0.

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






47. 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)






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






49. 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)






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