5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 15:57

264 STEP 4. Review the Knowledge You Need to Score High

(a)

∫ 0

− 2

g(x)dx

(b)

∫− 2

2

g(x)dx

(c)

∫− 2

0

5 g(x)dx

(d)

∫ 2

− 2

2 g(x)dx

18. Evaluate

∫ 1 / 2

0

dx

√

1 −x^2

.

19. Find
    dy
    dx
    ify=

∫sinx

cosx

(2t+1)dt.

20. Let fbe a continuous function defined on
    [0, 30] with selected values as shown below:

x 0 5 10 15 20 25 30

f(x) 1.4 2.6 3.4 4.1 4.7 5.2 5.7

Use a midpoint Riemann sum with three

subdivisions of equal length to find the

approximate value of

∫ 30

0

f(x)dx.

12.6 Cumulative Review Problems

(Calculator) indicates that calculators are
permitted.

21. Evaluate lim
    x→−∞

√

x^2 − 4

3 x− 9

.

22. Find
    dy
    dx
    atx=3ify=ln

∣∣

x^2 − 4

∣∣

.

23. The graph off′, the derivative off,
    − 6 ≤x≤8 is shown in Figure 12.6-1.

y

0 x

– 6 – 5 – 4 – 3 – 2 – (^1) – 1 123456
1
2
3

• 2


• 3

78

f′

Figure 12.6-1

(a) Find all values ofxsuch that fattains

a relative maximum or a relative

minimum.

(b) Find all values ofxsuch that fis

concave upward.

(c) Find all values ofxsuch that fhas a

change of concavity.

24. (Calculator) Given the equation
    9 x^2 + 4 y^2 − 18 x+ 16 y=11,
    find the points on the graph where the
    equation has a vertical or horizontal
    tangent.


25. (Calculator) Two corridors, one 6 feet
    wide and another 10 feet wide meet at a
    corner. (See Figure 12.6-2.) What is the
    maximum length of a pipe of negligible
    thickness that can be carried horizontally
    around the corner?

Pipe

6 ft.

10 ft.

Figure 12.6-2