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






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






3. The process of evaluating an indefinite integral






4. N(1-r)^x






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






6. 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






7. Intervals in which the second derivative is positive






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






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






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






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






12. The value of the function at a critical point






13. Having the limits or boundaries established






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






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






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






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






18. 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)






19. 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






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






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






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






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






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






25. 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)






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






27. The function that is integrated in an integral






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






29. 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)






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






31. 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))






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






33. 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)






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






35. A function whose rule is given by a fraction whose numerator and denominator are polynomials and whose denominator is not 0






36. d = v[( x2 - x1)² + (y2 - y1)²]






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






38. A function that possesses a finite integral; the function must be continuous on the interval of integration






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






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






41. Intervals on which the second derivative is negative






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






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






44. An undetermined constant added to every result of integration (the added +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 function that is continuous at every point on the interval






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






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






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






50. 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