5 Steps to a 5 AP Calculus BC 2019

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

Use a midpoint Riemann sum with three

subdivisions of equal length to find the

approximate value of

∫ 30

0

f(x)dx.

21.

∫∞

0

e−xdx

22.

∫ 0

−∞

dx

(4−x)^2

23.

∫ 1

0

lnxdx

24.

∫ 2

− 2

dx

√

4 −x^2

25.

∫ 8

− 1

dx

√ (^3) x
11.7 Cumulative Review Problems
(Calculator) indicates that calculators are
permitted.

26. Evaluate limx→−∞

√

x^2 − 4

3 x− 9

.

27. Find
    dy
    dx
    atx=3ify=ln

∣∣

x^2 − 4

∣∣

.

28. The graph off′, the derivative off,
    − 6 ≤x≤8 is shown in Figure 11.7-1.
    y

–6 –5 –4 –3 –2 –1^0123456 x

–1

1

2

3

–2

–3

78

f′

Figure 11.7-1

(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.

29. (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.
    30. (Calculator) Two corridors, one 6 feet
    wide and another 10 feet wide meet at a
    corner. (See Figure 11.7-2.) What is the
    maximum length of a pipe of negligible
    thickness that can be carried horizontally
    around the corner?

Figure 11.7-2

31. Evaluate limx→− 1
    1 +cosπx
    x^2 − 1

.

32. Determine the speed of an object moving
    along the path described byx= 3 − 2 t^2 ,
    y=t^2 +1 whent=

1

2

.

33.

∫

2 x

√

x+ 3 dx