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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]
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[pic]
E
D
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A
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