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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. 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)






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






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






4. 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






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






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






7. 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






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






9. 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))






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






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






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






13. 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






14. d = v[( x2 - x1)² + (y2 - y1)²]






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






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






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






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






19. 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)






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






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






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






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






24. 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.






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






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






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






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






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






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






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






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






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






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






35. 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)






36. A given value of x and f(x) used to find the constant of integration






37. The value of the function at a critical point






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






39. Intervals on which the second derivative is negative






40. 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






41. The process of evaluating an indefinite integral






42. The reciprocal of the sine function






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






44. The function that is integrated in an integral






45. N(1-r)^x






46. A²=(b²+c²)-2(ab)Cos(A)






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






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






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






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