Essential Calculus 2nd Edition by James Stewart Test Bank

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questions:
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Essay question
Description
Stewart_Essential Calc_2ET ch05sec01
MULTIPLE CHOICE
1. Determine a region whose area is equal to .
a.
b.
c.
d.
e.
ANS: E
MSC: Bimodal
PTS: 1
NOT: Section 5.1
DIF:
Medium
REF:
5.1.17
NUMERIC RESPONSE
1. By reading values from the given graph of , use five rectangles to find a lower estimate,
to the nearest whole number, for the area from 0 to 10 under the given graph of .
ANS: 21
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.1.1a
NOT: Section 5.1
2. The speed of a runner increased steadily during the first three seconds of a race. Her
speed at half-second intervals is given in the table. Find a lower estimate for the
distance that she traveled during these three seconds.
2.8
3.5
6.9
8.2
12.2
16.3
ANS: 16.8
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.1.9
NOT: Section 5.1
3. The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the
distance traveled by the car while the brakes are applied.Use a left sum with n = 7.
ANS: 19
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.1.13
NOT: Section 5.1
4. The velocity graph of a car accelerating from rest to a speed of 7 km/h over a period of
10 seconds is shown. Estimate to the nearest integer the distance traveled during this
period. Use a right sum with .
ANS: 37
PTS: 1
DIF: Medium
REF: 5.1.14
MSC: Numerical Response
NOT: Section 5.1
Stewart_Essential Calc_2ET ch05sec02
MULTIPLE CHOICE
1. Evaluate the Riemann sum for with four subintervals, taking the sample points to be
right endpoints.
a.
b.
c.
d.
e.
ANS: E
MSC: Bimodal
PTS: 1
NOT: Section 5.2
DIF:
Medium
2. Use the Midpoint Rule with n = 5 to approximate the integral.
Round your answer to three decimal places.
REF:
5.2.1
a.
b.
c.
d.
e.
ANS: E
MSC: Bimodal
PTS: 1
NOT: Section 5.2
DIF:
Medium
3. Use the Midpoint Rule with n = 10 to approximate the integral.
a.
b.
c.
d.
REF:
5.2.11
e.
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 5.2
DIF:
Medium
REF:
5.2.13
PTS: 1
NOT: Section 5.2
DIF:
Medium
REF:
5.2.40
4. If and , find .
a.
b.
c.
d.
e.
ANS: E
MSC: Bimodal
NUMERIC RESPONSE
1. A table of values of an increasing function is shown. Use the table to find an upper
estimate of
.
–45
–37
–27
9
10
23
ANS: –110
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.2.9
NOT: Section 5.2
2. Express the integral as a limit of sums. Then evaluate the limit.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.2.27
NOT: Section 5.2
3. Evaluate by interpreting it in terms of areas.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.2.31
NOT: Section 5.2
4. Evaluate by interpreting it in terms of areas.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.2.33
NOT: Section 5.2
5. Evaluate by interpreting it in terms of areas.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.2.34
NOT: Section 5.2
6. Given that , find .
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
Stewart_Essential Calc_2ET ch05sec03
MULTIPLE CHOICE
1. Evaluate the integral.
a.
b.
c.
d.
REF: 5.2.38
NOT: Section 5.2
e.
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 5.3
DIF:
Medium
REF: 5.3.2
DIF:
Medium
REF: 5.3.21
2. Evaluate the integral.
a.
b.
c.
d.
e.
ANS: A
MSC: Bimodal
PTS: 1
NOT: Section 5.3
3. Evaluate the integral.
a.
b.
c.
d.
e.
ANS: C
MSC: Bimodal
PTS: 1
NOT: Section 5.3
DIF:
Medium
REF: 5.3.38
4. The area of the region that lies to the right of the y-axis and to the left of the parabola
(the shaded region in the figure) is given by the integral .
Find the area..
a.
b.
c.
d.
e.
ANS: C
MSC: Bimodal
PTS: 1
NOT: Section 5.3
DIF:
Medium
REF: 5.3.49
5. The velocity function (in meters per second) is given for a particle moving along a line.
Find the distance traveled by the particle during the given time interval.
a.
68 m
b.
100 m
c.
64 m
d.
36 m
e.
72 m
ANS: A
MSC: Bimodal
PTS: 1
NOT: Section 5.3
DIF:
Medium
REF: 5.3.59b
6. The acceleration function (in m/) and the initial velocity are given for a particle moving
along a line. Find the velocity at time t and the distance traveled during the given time
interval.
a.
b.
c.
d.
e.
ANS: C
MSC: Bimodal
PTS: 1
NOT: Section 5.3
DIF:
Medium
REF: 5.3.61
7. The velocity of a car was read from its speedometer at ten-second intervals and
recorded in the table. Use the Midpoint Rule to estimate the distance traveled by the
car.
0
0
60
10
70
20
80
30
90
40
100
50
a.
1.8 miles
b.
0.6 miles
c.
0.8 miles
d.
1.2 miles
e.
2.4 miles
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 5.3
DIF:
Medium
REF: 5.3.63
Stewart_Essential Calc_2ET ch05sec04
MULTIPLE CHOICE
1. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the
function.
a.
b.
c.
d.
e.
ANS: A
MSC: Bimodal
none of these
PTS: 1
NOT: Section 5.4
DIF:
Medium
REF:
5.4.5
2. Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the
function.
a.
b.
c.
d.
e.
ANS: B
MSC: Bimodal
PTS: 1
NOT: Section 5.4
DIF:
Easy
3. Find the average value of the function on the given interval.
REF:
5.4.7
a.
b.
c.
d.
e.
ANS: A
MSC: Bimodal
PTS: 1
NOT: Section 5.4
DIF:
Medium
NUMERIC RESPONSE
1. Find the derivative of the function.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.4.6
NOT: Section 5.4
2. Find a function such that for x > 0 and some number a.
ANS: ; for
PTS: 1
DIF: Medium
MSC: Numerical Response
Stewart_Essential Calc_2ET ch05sec05
MULTIPLE CHOICE
REF: 5.3.63
NOT: Section 5.3
REF:
5.4.15
1. Evaluate the integral by making the given substitution.
a.
b.
c.
d.
e.
ANS: D
MSC: Bimodal
PTS: 1
NOT: Section 5.5
2. Evaluate the indefinite integral.
a.
b.
c.
DIF:
Medium
REF:
5.5.4
d.
e.
ANS: B
MSC: Bimodal
PTS: 1
NOT: Section 5.5
DIF:
Medium
REF:
5.5.20
DIF:
Medium
REF:
5.5.47
3. Evaluate the indefinite integral.
a.
b.
c.
d.
e.
ANS: A
MSC: Bimodal
PTS: 1
NOT: Section 5.5
4. Alabama Instruments Company has set up a production line to manufacture a new
calculator. The rate of production of these calculators after t weeks is
calculators per week. Production approaches 5,700 per week as time goes on, but
the initial production is lower because of the workers’ unfamiliarity with the new
techniques. Find the number of calculators produced from the beginning of the third
week to the end of the fourth week.
Round the answer to the nearest integer.
a.
b.
c.
d.
e.
f.
ANS: F
MSC: Bimodal
PTS: 1
NOT: Section 5.5
DIF:
Medium
NUMERIC RESPONSE
1. Evaluate the indefinite integral.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
2. Evaluate the definite integral.
REF: 5.5.33
NOT: Section 5.5
REF:
5.5.64
ANS: 0
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.5.46
NOT: Section 5.5
3. Evaluate the definite integral.
ANS:
PTS: 1
DIF: Medium
MSC: Numerical Response
REF: 5.5.51
NOT: Section 5.5
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