1



AP Calculus AB Fall Final Exam Review

1) Find the limit. [pic]

2) Find the limit of the function: f(x) = [pic] as x approaches [pic].

3) Evaluate: [pic]

4) Evaluate: [pic]

5) Find the limit: [pic]

6) Find the limit: [pic]

7) Let [pic]. Find the limit: [pic].

8) Find the limit: [pic].

9) Find the horizontal asymptote(s) of [pic]

10) Find the value(s) of x at which the curve [pic] has a vertical asymptote.

11) Find the limit: [pic]

12) Find the limit: [pic]

13) Find the value(s) of x at which the function f(x) = [pic] is discontinuous.

14) For what value of the constant c is the function f continuous on [pic]?

[pic]

15) At what value(s) of x is the function [pic] discontinuous?

16) Let [pic] and [pic]. Find [pic].

17) Find [pic].

18) Let[pic]. If f(x) is differentiable at x = 2, what is the value of a?

19) For the curve f(x) =[pic], find the slope of the secant line through the points (4, f(4)), and (25, f(25)).

20) Find the slope of the tangent to [pic] at x = 4.

21) Find the equation of the line tangent to [pic] at x = 2.

22) If f(x) = [pic], find the slope of the line tangent to f(x) at the point ((1, 36).

23) Find the slope of the line tangent to the curve [pic] at the point (1, 4).

24) For the curve[pic], find the slope of the tangent line at the point where x = 1.

25) Find an equation of the tangent line to [pic] at the point where x = 3.

26) If the tangent line to y = f (x) at (5, 1) also passes through the point (2, 7), then f '(5) = _______?

27) Given the graph of the derivative, sketch the original function on the same axes:

28) Estimate all value(s) of x (if any) that satisfy the Mean Value Theorem for the function [pic].

29) If y = [pic], then [pic]=

30) Find the acceleration at t = 2 given s(t) = [pic].

31) Find the derivative of [pic]

32) Find the interval where the function is concave down: [pic]

33) A box with a square base and open top must have a volume of 32,000 [pic]. Find the dimensions of the box which will minimize the amount of material used.

34) Given the graph of [pic] below, at which point is it true that [pic]

35) Find the critical number c for [pic] at which f(c) is not a local maximum and not a local minimum.

36) Find the x–coordinate of the point of inflection of the function [pic]

37) Given that [pic] has a relative maximum at x = 6, choose the correct statement.

A) [pic] is positive on the interval [pic]. B) [pic] is negative on the interval [pic]. C) [pic] is positive on the interval [pic]. D) [pic] is negative on the interval [pic].

38) Given that[pic] has critical numbers at x =1 and x = 3, find a and b.

39) The equation of motion is given for a particle, where s is in meters and t is in seconds. Find the acceleration after 4.5 seconds. [pic]

40) A particle’s position is given by [pic] for [pic]. When is the particle at rest?

41) Find the minimum value of [pic] on [pic].

42) What is the slope of the tangent line to [pic] at [pic]?

43) Two positive numbers, a and b, multiply to 18. If we wish to minimize 2a + b, what must the value of a be?

44) Find the point(s) of inflection, if any, of [pic].

45) If h(x) = f(g(x)), g(3) = 6, g’(3) = (8, [pic](3) = 2 and [pic](6) = 8, find [pic](3).

46) If y =[pic], calculate [pic].

47) Find the derivative of y = [pic].

48) Find [pic]: [pic].

49) Let [pic] and [pic]. Find the value of [pic] when x = 1.

50) Find the derivative: [pic]

51) What is[pic]? y = cos(5x)

52) Find [pic]. [pic]

-----------------------

[pic]

E

D

B

C

A

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download