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AP Calculus Final Exam Review Multiple Choice Section 3
1.
∫1 (8𝑥 3 − 3𝑥)𝑑𝑥 =
2.
If ∫𝑎 𝑓(𝑥)𝑑𝑥 = 𝑎 + 3𝑏, then ∫𝑎 (𝑓(𝑥) + 2)𝑑𝑥 =
3.
If 𝑓(𝑥) = −𝑥 4 + 𝑥 2 + 𝑥 2 , then 𝑓 ′ (−2) =
4.
The graph of 𝑦 = 8𝑥 4 − 12𝑥 3 + 12𝑥 2 + 32 is concave up for
5.
𝑏
𝑏
1
𝑑 𝑑𝑥
(tan3 𝑥 2 ) =
Questions 6-7 refer to the following situation:
3 2 1 -1
1
2
3
4
5
6
7
8
A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown above.
6.
For what value of t is the bug moving upwards?
7.
What is the total distance the bug traveled from t = 2 to t = 7?
–2
2
8. The graph of the derivative of f is shown in the figure above. Sketch a graph of f?
9. Let f be a differentiable function such that 𝑓(2) = 1 and 𝑓 ′ (2) = 3. If the tangent line to the graph of f at x = 1 is used to find an approximation to a zero of f, that approximation is y
3 2 1 x a 10.
b
The graph of the function f is shown in the figure above. What is lim 𝑓(𝑥)? What is lim 𝑓(𝑥)? Where is the function continuous? 𝑥→𝑎
𝑥→𝑏
2
11.
If 𝑓(𝑥) = cos(𝑒 −𝑥 ), then 𝑓 ′ (𝑥) =
12.
The area of the region enclosed by the graph of y = x2 + 2 and the line y = 11 is
13.
d2y If x + y = 36, what is the value of dx2 at the point (2,5)?
14.
The average value of sin x on the interval [–2,7] is
15.
2
2
What are all values of x for which the function f defined by f(x) = (x2 – 15)ex is decreasing?
16.
If the region enclosed by the y–axis, the line y = 3, and the curve y = x is revolved about the y–axis, the volume of the solid generated is
17.
If 𝑥 2 + 𝑦 = 5, then 𝑑𝑥 =
𝑑𝑦
P
R 18.
Q
In the figure above, PQ represents a 40-foot ladder with end P against a vertical wall and end Q on level ground. If the ladder is slipping down the wall, what is the distance RQ at 3 the instant when Q is moving along the ground 4 as fast as P is moving down the wall? 1
19. What is the x-coordinate of the point of inflection on the graph 𝑦 = 3 𝑥 3 + 10𝑥 + 25?
20. lim
𝑛→∞
5𝑛3 +6𝑛2 +2𝑛−1 8−3𝑛−6𝑛2
is
21. Evaluate:
22.
𝑑
(
5
𝑑𝑥 5−𝑥 3
lim
𝑛2 +𝑛−6
𝑛→−3 𝑛2 −9
)=
23. If 𝑓(𝑥) = −√𝑒 𝑥 , then 𝑓′(ln 3) =
24. At x = 2, is the function given by 𝑓(𝑥) = {
𝑥3, 𝑥 < 2 continuous? Is it differentiable? 4𝑥, 𝑥 ≥ 2
25. An equation of the line tangent to the graph of 𝑓(𝑥) = 3𝑥 2 (4 − 3𝑥)2 at the point (1, -1) is
26. Shown above is a slope field for which of the following differential equations? dy x3 dy x 2 dy x dy x 2 dy x3 (A) (B) (C) (D) (E) 2 dx y dx y dx y dx y dx y 2
There will also be 1 group of 4 free response questions.