Name: ________________________ Class: ___________________ Date: __________
ID: A
Final Exam Review
Short Answer
1. Solve the following equation for x .
10. Use implicit differentiation to find
log 6 x  log6 (x  5 )  1
ÊÁ 3,1ˆ˜ .
Ë ¯
2. Use the functions f (x )  x  2 and g (x )  9x  7 to
1
find the function ÁÊË f û g ˆ˜¯ (x ) .
6xy  3 lny  18
11. Write the following expression in algebraic form.
3. Find an equation of the tangent line to the graph of
Ê ˆ
y  ln ÁÁÁ x 2 ˜˜˜ at the point (1,0).
Ë ¯
Ê
Ê
ˆˆ
cos ÁÁÁÁ arcsin ÁÁÁ 7x 4 ˜˜˜ ˜˜˜˜
Ë
¯¯
Ë
12. Find the indefinite integral.
4. Find the indefinite integral.
 4x 2  9
x
dy
at the point
dx
 cos 3x e sin 3x dx
dx
13. Write the following expression as a logarithm of a
single quantity.
ÊÁ
11 ˆ˜
5. Evaluate the expression cos ÁÁÁÁ arcsin ˜˜˜˜ without
61 ¯
Ë
Ê
ˆ
15 ln x  14lnÁÁÁ x 2  5 ˜˜˜
Ë
¯
using a calculator.
6. Find the derivative of the function
ÊÁ 13x ˆ˜
˜˜ .
f (x )  lnÁÁÁÁ 2
˜˜

6
x
Ë
¯

14. Find tan 10 d  .
15. Find the integral
dy
at the point ÊÁË 2, 1 ˆ˜¯ for the equation
dx
x  y 3  6y 2  7 .
 t 4  256 dt.
t
7. Find
ÊÁ 5x
ˆ
ÁÁ e  1 ˜˜˜
Á
˜˜ .
16. Differentiate the function f (x )  ln ÁÁ 3x
ÁÁ e  1 ˜˜˜
Ë
¯
8. Find the indefinite integral.

5xe
4x
17. Write the following expression in algebraic form.
2
dx
sin ÁÊË arccos (8x) ˜ˆ¯
Ê
ˆ
9. Differentiate the function f(x)  ln ÁÁÁ 3x 2  4x  8 ˜˜˜ .
Ë
¯
18. Find the indefinite integral.

1
1
9  16x 2
dx
Name: ________________________
ID: A
19. Find the derivative of the function
y  ln
21. Find all points of inflection on the graph of
f (x )  (6x  5) ln x,x  0 .
x 2  11 .
22. Find f 1 (x ) if f (x )  x 3  7.
20. Find the following limit if it exists: lim ln (x  2 ) .
x2

Use  when appropriate.
23. Find

x 2  9x  18
dx .
x3
24. Find the indefinite integral.
27. Find

cos (14 )
d
sin (14 )
x
 x  16 dx .
28. Use logarithmic differentiation to find
25. Find the derivative of the function f (x )  x 3 e x .
26. Use logarithmic differentiation to find
y
dy
.
dx
y  x 5x
2
5x  3
(3x  2)
2
dy
.
dx
Name: ________________________
ID: A
29.
Test Two Review Cal 2 Fall 13
Short Answer
1. Set up the definite integral that gives the area of the region bounded by the graph of
.
2. Find the area of the region bounded by the equations by integrating (i) with respect to x and
(ii) with respect to y.
3. Find the area of the region bounded by equations by integrating (i) with respect to x and
(ii) with respect to y.
4. Find the area of the region bounded by the graphs of the algebraic functions.
5. Find the area of the region bounded by the graphs of the algebraic functions.
3
and
Name: ________________________
ID: A
6. Find the area of the region bounded by the graphs of the equations.
7. Find the area of the region bounded by the graphs of the function
. Round your
answer to three decimal places.
8. Find the area of the region bounded by the graphs of the equations.
.
9. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations
, and
about the line
.
10. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations
, and
about the line
.
11. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the
.
line
12. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the
.
line
13. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the
line
.
14. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the
-axis.
15. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the
-axis.
4
Name: ________________________
ID: A
16. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the
-axis. Verify your results using the integration capabilities of a graphing utility.
17. A tank on the wing of a jet aircraft is formed by revolving the region bounded by the graph of
and
about the x-axis, where x and y are measured in meters. Find the volume of the tank. Round
the x-axis
your answer to two decimal places.
18. Use the shell method to set up and evaluate the integral
revolving the plane region about the y-axis.
that gives the volume of the solid generated by
19. Use the shell method to set up and evaluate an integral that gives the volume of the solid generated by revolving
the plane region about the y-axis.
20. Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving
about the x-axis.
the plane region bounded by
21. Use the shell method to find the volume of the solid generated by revolving the plane region bounded by
about the line
.
22. Use the disk or shell method to find the volume of the solid generated by revolving the region bounded by the
.
graphs of the equations about the line
5
Name: ________________________
ID: A
23. Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the
about the x-axis.
graphs of the equations
24. Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the
about the line
.
graphs of the equations
25. Find the arc length of the graph of the function
over the interval [12, 14].
26. Find the arc length of the graph of the function
over the interval [1,2].
27. Find the arc length of the graph of the function
over the interval
.
28. Find the area of the surface generated by revolving the curve about the x-axis.
.
29. Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of
about the x-axis.
30. Set up and evaluate the definite integral for the area of the surface formed by revolving the graph of
about the y-axis. Round your answer to three decimal places.
6
Name: ________________________
ID: A
31. Determine the work done by lifting a 140 pound bag of sugar 8 feet.
32. A force of 5 pounds compresses a 20-inch spring 4 inches. How much work is done in compressing the spring
from a length of 14 inches to a length of 11 inches?
33. A tank with a base of 4 feet by 3 feet and a height of 4 feet is full of water. The water weighs 62.4 pounds per
cubic foot. How much work is done in pumping water out over the top edge in order to empty half of the tank.
Round your answer to one decimal place.
34. Find the center of mass of the point masses lying on the x-axis.
35. Find the center of mass of the point masses lying on the x-axis.
36. Find the center of mass of the point masses lying on the x-axis.
37. Consider a beam of length
feet with a fulcrum x feet from one end as shown in the figure. Two objects
weighing 48 pounds and 108 pounds are placed at opposite ends of the beam. Find x (the distance between the
fulcrum and the object weighing 48 pounds) such that the system is equilibrium.
7
Name: ________________________
ID: A
38. Find the center of mass of the given system of point masses.
39. Find the center of mass of the given system of point masses.
40. Find
for the lamina of uniform density
bounded by the graphs of the equations
.
Test 3 Calculus II
Short Answer
1. Find the indefinite integral.
2. Solve.
3. Determine whether the improper integral
diverges or converges. Evaluate the integral if it converges.
4. Find the definite integral.
8
Name: ________________________
ID: A
5. Evaluate the definite integral
.
6. Find the indefinite integral.
7. Find the indefinite integral.
8. Use substitution to find the integral
.
9. Find the indefinite integral by making the substitution
10. Find the indefinite integral.
11. Find the indefinite integral.
12. Use partial fractions to find
.
13. Find the indefinite integral.
9
.
Name: ________________________
ID: A
14. Use partial fractions to find the integral
.
15. Find the indefinite integral.
16. Evaluate the limit
using L'Hopital's Rule if necessary.
17. Determine whether the improper integral
18. Evaluate the limit
diverges or converges. Evaluate the integral if it converges.
using L'Hopital's Rule if necessary.
19. Determine whether the improper integral
diverges or converges. Evaluate the integral if it
converges.
20. Determine whether the improper integral
diverges or converges. Evaluate the integral if it
converges.
21. Find the indefinite integral.
22. Find the indefinite integral.
23. Find the indefinite integral.
10
Name: ________________________
ID: A
24. Find the indefinite integral.
25. Evaluate the limit
using L'Hopital's Rule if necessary.
.
26. Evaluate the definite integral
27. Evaluate the limit
using L'Hopital's Rule if necessary.
28. Evaluate the limit
using L'Hopital's Rule if necessary.
Test 4 Review Cal 2
Short Answer
1. Write the first three terms of the sequence.
2. Write an expression for the nth term of the sequence
.
3. Find the sum of the convergent series
4. Find the sum of the convergent series
5. Write the repeating decimal
.
as a geometric series.
6. Use the Integral Test to determine the convergence or divergence of the series.
11
Name: ________________________
ID: A
7. Use the Integral Test to determine the convergence or divergence of the series.
8. Use Theorem 9.11 to determine the convergence or divergence of the series.
9. Find the positive values of
for which the series
converges.
10. Use the Direct Comparison Test to determine the convergence or divergence of the series
11. Use the Limit Comparison Test to determine the convergence or divergence of the series
12. Use the Limit Comparison Test to determine the convergence or divergence of the series
13. Use the Alternating Series Test (if possible) to determine whether the series
.
.
converges or
diverges?
14. Determine whether the series
15. Determine whether the series
converges conditionally or absolutely, or diverges.
converges absolutely, converges conditionally, or diverges.
12
Name: ________________________
16.
Determine whether the series
ID: A
converges conditionally or absolutely, or diverges.
17. Use the Ratio Test to determine the convergence or divergence of the series.
18. Use the Root Test to determine the convergence or divergence of the series.
19. Identify the most appropriate test to be used to determine whether the series
converges or diverges.
20. Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test
used.
21. Determine the convergence or divergence of the series using any appropriate test from this chapter. Identify the test
used.
22. Identify the most appropriate test to be used to determine whether the series
23. State where the power series
is centered.
24. Find the radius of convergence of the power series.
13
converges or diverges.
Name: ________________________
ID: A
25. Find the directrix of the parabola given by
.
.
26. Find the vertices of the ellipse given by
27. Find an equation of the ellipse with vertices
and eccentricity
.
28. Find the center, foci, and vertices of the hyperbola.
29. Find an equation of the hyperbola with vertices
and asymptotes
.
30. Write the corresponding rectangular equation for the curve represented by the parametric equations
by eliminating the parameter.
31. Use the result, "the set of parametric equations for the line passing through
and
is
" to find a set of parametric equations for the line passing through
.
and
32. Find a set of parametric equations for the rectangular equation
point
.
33. Find
that satisfies the condition
.
34. Find the second derivative
of the parametric equations
Test 4 Review Cal 2
Answer Section
14
.
at the
Name: ________________________
ID: A
SHORT ANSWER
1. ANS:
PTS: 1
DIF: Medium
REF: 9.1.10
OBJ: Write the first terms of a sequence given its nth term
NOT: Section 9.1
2. ANS:
PTS: 1
DIF: Easy
REF: 9.1.74
OBJ: Write an expression for the nth term of sequence
NOT: Section 9.1
3. ANS:
MSC: Skill
MSC: Skill
PTS: 1
MSC: Skill
4. ANS:
DIF: Difficult
NOT: Section 9.2
REF: 9.2.47
OBJ: Calculate the sum of a geometric series
PTS: 1
MSC: Skill
5. ANS:
DIF: Difficult
NOT: Section 9.2
REF: 9.2.49
OBJ: Calculate the sum of a telescoping series
PTS: 1
DIF: Medium
REF: 9.2.55a
OBJ: Write a repeating decimal as a geometric series
NOT: Section 9.2
6. ANS:
diverges
PTS: 1
DIF: Medium
REF: 9.3.2
OBJ: Test a series for convergence using the Integral Test
NOT: Section 9.3
7. ANS:
diverges
PTS: 1
DIF: Medium
REF: 9.3.16
OBJ: Test a series for convergence using the Integral Test
NOT: Section 9.3
8. ANS:
diverges
15
MSC: Skill
MSC: Skill
MSC: Skill
Name: ________________________
PTS: 1
MSC: Skill
9. ANS:
converges for
DIF: Medium
NOT: Section 9.3
ID: A
REF: 9.3.40
PTS: 1
DIF: Difficult
REF: 9.3.57
OBJ: Test a series for convergence using the Integral Test
NOT: Section 9.3
10. ANS:
OBJ: Test a p-series for convergence
MSC: Skill
PTS: 1
DIF: Medium
REF: 9.4.12
OBJ: Test a series for convergence using the Direct Comparison Test
MSC: Skill
NOT: Section 9.4
11. ANS:
PTS: 1
DIF: Easy
REF: 9.4.15
OBJ: Test a series for convergence using the Limit Comparison Test
MSC: Skill
NOT: Section 9.4
12. ANS:
PTS: 1
DIF: Medium
REF: 9.4.32
OBJ: Test a series for convergence using the Limit Comparison Test
MSC: Skill
NOT: Section 9.4
13. ANS:
PTS: 1
DIF: Easy
REF: 9.5.20
OBJ: Test an alternating series for convergence
NOT: Section 9.5
14. ANS:
MSC: Skill
The series converges conditionally but does not converge absolutely.
PTS: 1
DIF: Easy
REF: 9.5.56
OBJ: Test a series for absolute/conditional convergence
NOT: Section 9.5
15. ANS:
PTS: 1
DIF: Easy
REF: 9.5.57
16
MSC: Skill
Name: ________________________
ID: A
OBJ: Test a series for absolute/conditional convergence
NOT: Section 9.5
16. ANS:
MSC: Skill
The series converges conditionally but does not converge absolutely.
PTS: 1
DIF: Medium
REF: 9.5.67
OBJ: Test a series for absolute/conditional convergence
NOT: Section 9.5
17. ANS:
converges
PTS: 1
DIF: Medium
REF: 9.6.24
OBJ: Test a series for convergence using the Ratio Test
NOT: Section 9.6
18. ANS:
diverges
PTS: 1
DIF: Easy
REF: 9.6.37
OBJ: Test a series for convergence using the Root Test
NOT: Section 9.6
19. ANS:
MSC: Skill
MSC: Skill
MSC: Skill
PTS: 1
DIF: Easy
REF: 9.6.51
OBJ: Identify the most appropriate test to be used to test a series for convergence
MSC: Skill
NOT: Section 9.6
20. ANS:
PTS: 1
DIF: Medium
REF: 9.6.51
OBJ: Identify the most appropriate test to be used to test a series for convergence
MSC: Skill
NOT: Section 9.6
21. ANS:
diverges; Theorem 9.9 (nth Term Test for Divergence)
PTS: 1
DIF: Medium
REF: 9.6.55
OBJ: Identify the most appropriate test to be used to test a series for convergence
MSC: Skill
NOT: Section 9.6
22. ANS:
PTS: 1
DIF: Easy
REF: 9.6.56
OBJ: Identify the most appropriate test to be used to test a series for convergence
MSC: Skill
NOT: Section 9.6
23. ANS:
4
PTS: 1
DIF: Easy
REF: 9.8.3
17
OBJ: Identify the center of a power series
Name: ________________________
MSC: Skill
24. ANS:
10
ID: A
NOT: Section 9.8
PTS: 1
DIF: Easy
REF: 9.8.8
OBJ: Identify the radius of convergence of a power series
NOT: Section 9.8
25. ANS:
MSC: Skill
PTS: 1
DIF: Medium
REF: 10.1.13
OBJ: Identify features of the graph of a parabola from its equation
MSC: Skill
NOT: Section 10.1
26. ANS:
PTS: 1
DIF: Difficult
REF: 10.1.33
OBJ: Identify features of the graph of an ellipse from its equation
MSC: Skill
NOT: Section 10.1
27. ANS:
PTS: 1
DIF: Medium
REF: 10.1.40
OBJ: Write the equation of an ellipse with specified properties
NOT: Section 10.1
28. ANS:
MSC: Skill
PTS: 1
DIF: Medium
REF: 10.1.47
OBJ: Identify features of the graph of a hyperbola from its equation
MSC: Skill
NOT: Section 10.1
29. ANS:
PTS: 1
DIF: Medium
REF: 10.1.57
OBJ: Write the equation of a hyperbola with specified properties
MSC: Skill
NOT: Section 10.1
30. ANS:
PTS: 1
DIF: Medium
REF: 10.2.12
OBJ: Convert parametric equations to a rectangular equation
NOT: Section 10.2
31. ANS:
18
MSC: Skill
Name: ________________________
ID: A
PTS: 1
DIF: Medium
REF: 10.2.43
OBJ: Write parametric equations for a rectangular equation
NOT: Section 10.2
32. ANS:
PTS: 1
DIF: Medium
REF: 10.2.55
OBJ: Write parametric equations for a rectangular equation
NOT: Section 10.2
33. ANS:
PTS: 1
DIF: Medium
REF: 10.3.1
OBJ: Differentiate a curve given in parametric form
NOT: Section 10.3
34. ANS:
MSC: Skill
MSC: Skill
MSC: Skill
PTS: 1
DIF: Medium
REF: 10.3.9
OBJ: Calculate the second derivative of a curve given in parametric form
MSC: Skill
NOT: Section 10.3
Test 3 Calculus II
Answer Section
SHORT ANSWER
1. ANS:
PTS: 1
DIF: Easy
REF: 8.3.5
OBJ: Evaluate an indefinite integral involving powers of sines and cosines
MSC: Skill
NOT: Section 8.3
2. ANS:
PTS: 1
MSC: Skill
3. ANS:
diverges
PTS: 1
DIF: Medium
NOT: Section 8.3
REF: 8.3.45
DIF: Easy
REF: 8.8.11
19
OBJ: Solve a differential equation
Name: ________________________
ID: A
OBJ: Evaluate an improper integral if it converges
NOT: Section 8.8
4. ANS:
72
MSC: Skill
PTS: 1
DIF: Medium
REF: 8.1.69
OBJ: Evaluate a definite integral using substitution
NOT: Section 8.1
5. ANS:
MSC: Skill
PTS: 1
DIF: Medium
REF: 8.5.29
OBJ: Evaluate the definite integral of a function using partial fractions with linear factors
MSC: Skill
NOT: Section 8.5
6. ANS:
PTS: 1
DIF: Medium
REF: 8.1.24
OBJ: Evaluate the indefinite integral of an improper fraction
NOT: Section 8.1
7. ANS:
MSC: Skill
PTS: 1
DIF: Medium
REF: 8.3.27
OBJ: Evaluate an indefinite integral involving powers of secants and tangents
MSC: Skill
NOT: Section 8.3
8. ANS:
PTS: 1
DIF: Medium
REF: 8.5.41
OBJ: Evaluate the indefinite integral of a function using a substitution and partial fractions
MSC: Skill
NOT: Section 8.5
9. ANS:
PTS: 1
DIF: Medium
REF: 8.4.9
OBJ: Evaluate the indefinite integral of a function using a secant substitution
MSC: Skill
NOT: Section 8.4
10. ANS:
20
Name: ________________________
ID: A
PTS: 1
DIF: Medium
REF: 8.2.20
OBJ: Evaluate the indefinite integral of a function using integration by parts
MSC: Skill
NOT: Section 8.2
11. ANS:
PTS: 1
DIF: Medium
REF: 8.3.34
OBJ: Evaluate an indefinite integral involving powers of secants and tangents
MSC: Skill
NOT: Section 8.3
12. ANS:
PTS: 1
DIF: Easy
REF: 8.5.7
OBJ: Evaluate the indefinite integral of a function using partial fractions with linear factors
MSC: Skill
NOT: Section 8.5
13. ANS:
PTS: 1
DIF: Medium
REF: 8.1.23
OBJ: Evaluate the indefinite integral of an improper fraction
NOT: Section 8.1
14. ANS:
MSC: Skill
PTS: 1
DIF: Easy
REF: 8.5.19
OBJ: Evaluate the indefinite integral of a function using partial fractions with linear factors
MSC: Skill
NOT: Section 8.5
15. ANS:
PTS: 1
DIF: Medium
REF: 8.3.10
OBJ: Evaluate an indefinite integral involving powers of sines and cosines
MSC: Skill
NOT: Section 8.3
16. ANS:
0
PTS: 1
DIF: Easy
REF: 8.7.36
OBJ: Evaluate the limit of a function using L'Hopital's Rule for infinity/infinity form
MSC: Skill
NOT: Section 8.7
17. ANS:
21
Name: ________________________
ID: A
PTS: 1
DIF: Medium
REF: 8.8.39
OBJ: Evaluate an improper integral if it converges
NOT: Section 8.8
18. ANS:
0
MSC: Skill
PTS: 1
DIF: Easy
REF: 8.7.29
OBJ: Evaluate the limit of a function using L'Hopital's Rule for infinity/infinity form
MSC: Skill
NOT: Section 8.7
19. ANS:
PTS: 1
DIF: Easy
REF: 8.8.46
OBJ: Evaluate an improper integral if it converges
NOT: Section 8.8
20. ANS:
PTS: 1
DIF: Difficult
REF: 8.8.28
OBJ: Evaluate an improper integral if it converges
NOT: Section 8.8
21. ANS:
MSC: Skill
MSC: Skill
PTS: 1
DIF: Medium
REF: 8.3.14
OBJ: Evaluate an indefinite integral involving powers of sines and cosines
MSC: Skill
NOT: Section 8.3
22. ANS:
PTS: 1
DIF: Medium
REF: 8.1.15
OBJ: Evaluate the indefinite integral of a function using substitution
MSC: Skill
NOT: Section 8.1
23. ANS:
PTS: 1
DIF: Medium
REF: 8.1.20
OBJ: Evaluate the indefinite integral of a function using substitution
MSC: Skill
NOT: Section 8.1
24. ANS:
22
Name: ________________________
ID: A
PTS: 1
DIF: Medium
REF: 8.4.34
OBJ: Evaluate the indefinite integral of a function using a tangent substitution
MSC: Skill
NOT: Section 8.4
25. ANS:
PTS: 1
DIF: Easy
REF: 8.7.23
OBJ: Evaluate the limit of a function using L'Hopital's Rule for 0/0 form
MSC: Skill
NOT: Section 8.7
26. ANS:
0
PTS: 1
DIF: Medium
REF: 8.1.66
OBJ: Evaluate a definite integral using substitution
NOT: Section 8.1
27. ANS:
MSC: Skill
PTS: 1
DIF: Easy
REF: 8.7.36
OBJ: Evaluate the limit of a function using L'Hopital's Rule for 0/0 form
MSC: Skill
NOT: Section 8.7
28. ANS:
0
PTS: 1
DIF: Easy
REF: 8.7.13
OBJ: Evaluate the limit of a function using L'Hopital's Rule for 0/0 form
MSC: Skill
NOT: Section 8.7
Test Two Review Cal 2 Fall 13
Answer Section
SHORT ANSWER
1. ANS:
PTS: 1
DIF: Easy
REF: 7.1.2
OBJ: Write the definite integrals needed to calculate the area of a bounded region
MSC: Skill
NOT: Section 7.1
2. ANS:
23
Name: ________________________
ID: A
PTS: 1
DIF: Medium
REF: 7.1.17b
OBJ: Calculate the area of a region bounded by two curves
NOT: Section 7.1
3. ANS:
PTS: 1
DIF: Medium
REF: 7.1.18a
OBJ: Calculate the area of a region bounded by two curves
NOT: Section 7.1
4. ANS:
PTS: 1
DIF: Medium
REF: 7.1.24
OBJ: Calculate the area of a region bounded by two curves
NOT: Section 7.1
5. ANS:
PTS: 1
DIF: Medium
REF: 7.1.30
OBJ: Calculate the area of a region bounded by two curves
NOT: Section 7.1
6. ANS:
PTS: 1
DIF: Medium
REF: 7.1.44b
OBJ: Calculate the area of a region bounded by several curves
NOT: Section 7.1
7. ANS:
31.308
PTS: 1
DIF: Medium
REF: 7.1.44b
OBJ: Calculate the area of a region bounded by several curves
NOT: Section 7.1
8. ANS:
PTS: 1
MSC: Application
9. ANS:
PTS: 1
DIF: Medium
NOT: Section 7.1
REF: 7.1.48
DIF: Difficult
REF: 7.2.12c
24
MSC: Application
MSC: Application
MSC: Application
MSC: Application
MSC: Application
MSC: Application
OBJ: Calculate the area between two curves
Name: ________________________
ID: A
OBJ: Calculate the volume using the washer method of the solid formed by revolving a region about a horizontal
line MSC:
Application
NOT: Section 7.2
10. ANS:
PTS: 1
DIF: Difficult
REF: 7.2.12d
OBJ: Calculate the volume using the disk method of the solid formed by revolving a region about a vertical line
MSC: Application NOT: Section 7.2
11. ANS:
PTS: 1
DIF: Medium
REF: 7.2.15
OBJ: Calculate the volume using the washer method of the solid formed by revolving a region about a horizontal
line MSC:
Application
NOT: Section 7.2
12. ANS:
PTS: 1
DIF: Medium
REF: 7.2.16
OBJ: Calculate the volume using the disk method of the solid formed by revolving a region about a horizontal
line MSC:
Application
NOT: Section 7.2
13. ANS:
PTS: 1
DIF: Medium
REF: 7.2.18
OBJ: Calculate the volume using the washer method of the solid formed by revolving a region about a horizontal
line MSC:
Application
NOT: Section 7.2
14. ANS:
PTS: 1
DIF: Medium
REF: 7.2.23
OBJ: Calculate the volume using the disk method of the solid formed by revolving a region about the x-axis
MSC: Application NOT: Section 7.2
15. ANS:
PTS: 1
DIF: Medium
REF: 7.2.25
OBJ: Calculate the volume using the disk method of the solid formed by revolving a region about the x-axis
MSC: Application NOT: Section 7.2
16. ANS:
25
Name: ________________________
ID: A
PTS: 1
DIF: Medium
REF: 7.2.33
OBJ: Calculate the volume using the disk method of the solid formed by revolving a region about the x-axis
MSC: Application NOT: Section 7.2
17. ANS:
0.01 m3
PTS: 1
DIF: Medium
REF: 7.2.63
OBJ: Calculate the volume using the disk method of the solid formed by revolving a region about the x-axis
MSC: Application NOT: Section 7.2
18. ANS:
PTS: 1
DIF: Easy
REF: 7.3.3
OBJ: Calculate the volume using the shell method of the solid formed by revolving a region about the y-axis
MSC: Application NOT: Section 7.3
19. ANS:
PTS: 1
DIF: Medium
REF: 7.3.8
OBJ: Calculate the volume using the shell method of the solid formed by revolving a region about the y-axis
MSC: Application NOT: Section 7.3
20. ANS:
PTS: 1
DIF: Medium
REF: 7.3.22
OBJ: Calculate the volume using the shell method of the solid formed by revolving a region about the x-axis
MSC: Application NOT: Section 7.3
21. ANS:
PTS: 1
DIF: Medium
REF: 7.3.26
OBJ: Calculate the volume using the shell method of the solid formed by revolving a region about a vertical line
MSC: Application NOT: Section 7.3
22. ANS:
PTS: 1
DIF: Medium
REF: 7.3.29a
OBJ: Calculate volumes of revolution by choosing an appropriate method
MSC: Application NOT: Section 7.3
23. ANS:
PTS: 1
DIF: Medium
REF: 7.3.29a
26
Name: ________________________
ID: A
OBJ: Calculate volumes of revolution by choosing an appropriate method
MSC: Application NOT: Section 7.3
24. ANS:
PTS: 1
DIF: Difficult
REF: 7.3.29c
OBJ: Calculate volumes of revolution by choosing an appropriate method
MSC: Application NOT: Section 7.3
25. ANS:
PTS: 1
DIF: Medium
REF: 7.4.5
OBJ: Calculate the arc length of a curve over a given interval
NOT: Section 7.4
26. ANS:
PTS: 1
DIF: Medium
REF: 7.4.9
OBJ: Calculate the arc length of a curve over a given interval
NOT: Section 7.4
27. ANS:
PTS: 1
DIF: Medium
REF: 7.4.15
OBJ: Calculate the arc length of a curve over a given interval
NOT: Section 7.4
28. ANS:
PTS: 1
DIF: Medium
REF: 7.4.37
OBJ: Calculate the area of a solid of revolution
NOT: Section 7.4
29. ANS:
PTS: 1
DIF: Easy
REF: 7.4.40
OBJ: Calculate the area of a solid of revolution
NOT: Section 7.4
30. ANS:
5.33
27
MSC: Application
MSC: Application
MSC: Application
MSC: Application
MSC: Application
Name: ________________________
ID: A
PTS: 1
DIF: Medium
REF: 7.4.44
OBJ: Calculate the area of a solid of revolution
NOT: Section 7.4
31. ANS:
1,120 ft-lb
PTS: 1
DIF: Easy
REF: 7.5.1
OBJ: Calculate the work done by a constant force
NOT: Section 7.5
32. ANS:
28.125 ft-lb
PTS: 1
DIF: Medium
REF: 7.5.6
OBJ: Calculate work in problems involving springs
NOT: Section 7.5
33. ANS:
1,497.6 ft-lb
MSC: Application
MSC: Application
MSC: Application
PTS: 1
DIF: Medium
REF: 7.5.17
OBJ: Calculate work in problems involving pumping liquids from containers
MSC: Application NOT: Section 7.5
34. ANS:
PTS: 1
DIF: Easy
REF: 7.6.1
OBJ: Calculate the center of mass in a one-dimensional system
MSC: Application NOT: Section 7.6
35. ANS:
PTS: 1
DIF: Easy
REF: 7.6.2
OBJ: Calculate the center of mass in a one-dimensional system
MSC: Application NOT: Section 7.6
36. ANS:
PTS: 1
DIF: Easy
REF: 7.6.3
OBJ: Calculate the center of mass in a one-dimensional system
MSC: Application NOT: Section 7.6
37. ANS:
9 feet
PTS: 1
DIF: Easy
REF: 7.6.7
OBJ: Calculate the center of mass in a one-dimensional system
MSC: Application NOT: Section 7.6
38. ANS:
28
Name: ________________________
ID: A
PTS: 1
DIF: Medium
REF: 7.6.9
OBJ: Calculate the center of mass in a two-dimensional system
MSC: Application NOT: Section 7.6
39. ANS:
PTS: 1
DIF: Medium
REF: 7.6.11
OBJ: Calculate the center of mass in a two-dimensional system
MSC: Application NOT: Section 7.6
40. ANS:
PTS: 1
DIF: Medium
REF: 7.6.15
OBJ: Calculate the center of mass for a lamina formed by curves
MSC: Application NOT: Section 7.6
3
Evaluate the integral

3
13
dx.
9  x2
29
ID: A
Final Exam Review
Answer Section
SHORT ANSWER
1. ANS:
1,6
PTS: 1
MSC: Skill
2. ANS:
x5
9
DIF: Medium
NOT: Section 5.5
REF: 5.5.24b
PTS: 1
DIF: Easy
REF: 5.3.93
OBJ: Construct the inverse of a composition of functions
NOT: Section 5.3
3. ANS:
y  2 (x  1 )
OBJ: Solve a logarithmic equation
MSC: Skill
PTS: 1
DIF: Medium
REF: 5.1.43
OBJ: Write an equation of a line tangent to the graph of a function at a specified point
MSC: Skill
NOT: Section 5.1
4. ANS:
1  2

ln 4x  9   C
8 
PTS: 1
DIF: Medium
REF: 5.2.7
OBJ: Evaluate the indefinite integral of a function involving logarithms
MSC: Skill
NOT: Section 5.2
5. ANS:
60
61
PTS: 1
DIF: Medium
REF: 5.6.18b
OBJ: Evaluate an expression involving an inverse trigonometric expression
MSC: Skill
NOT: Section 5.6
6. ANS:
1
2x
f  (x )   2
x x 6
PTS: 1
DIF: Medium
REF: 5.1.57
OBJ: Differentiate a logarithmic function using the chain rule and quotient rule
MSC: Skill
NOT: Section 5.1
1
ID: A
7. ANS:
1

9
PTS: 1
DIF: Medium
REF: 5.3.85
OBJ: Evaluate a derivative at a point using the inverse function
MSC: Skill
NOT: Section 5.3
8. ANS:
2
5
 e 4x  C
8
PTS: 1
DIF: Medium
REF: 5.4.103
OBJ: Evaluate the indefinite integral of an exponential function using substitution
MSC: Skill
NOT: Section 5.4
9. ANS:
6x  4
3x 2  4x  8
PTS: 1
DIF: Medium
REF: 5.1.50
OBJ: Differentiate a logarithmic function using the chain rule
NOT: Section 5.1
10. ANS:
2

7
MSC: Skill
PTS: 1
DIF: Medium
REF: 5.1.88
OBJ: Differentiate an equation using implicit differentiation and evaluate at a specified point
MSC: Skill
NOT: Section 5.1
11. ANS:
1  49x 8
PTS: 1
DIF: Medium
REF: 5.6.27
OBJ: Convert an inverse trigonometric expression to an algebraic expression
MSC: Skill
NOT: Section 5.6
12. ANS:
1 sin 3x
e
C
3
PTS: 1
DIF: Medium
REF: 5.4.125
OBJ: Evaluate the indefinite integral of an exponential function using substitution
MSC: Skill
NOT: Section 5.4
2
ID: A
13. ANS:
ÊÁ
ÁÁ
ÁÁ
x 15
Á
ln ÁÁÁ
14
ÁÁ ÊÁ 2
ÁÁ ÁÁ x  5 ˆ˜˜˜
ÁË
¯
Ë
ˆ˜
˜˜
˜˜
˜˜
˜˜
˜˜
˜˜
˜
¯
PTS: 1
DIF: Medium
REF: 5.1.35
OBJ: Write a logarithmic expression as a single quantity
NOT: Section 5.1
14. ANS:
1
tan 10 d    ln cos 10   C
10
MSC: Skill

PTS: 1
DIF: Easy
REF: 5.2.32
OBJ: Evaluate the indefinite integral of a function involving logarithms
MSC: Skill
NOT: Section 5.2
15. ANS:
1
t2
arctan dt  C
32
16
PTS: 1
DIF: Medium
REF: 5.7.11
OBJ: Evaluate the indefinite integral involving an inverse trigonometric function
MSC: Skill
NOT: Section 5.7
16. ANS:
5e 5x
3e 3x

e 5x  1 e 3x  1
PTS: 1
DIF: Medium
REF: 5.4.52
OBJ: Differentiate a logarithmic function using the chain rule
NOT: Section 5.4
17. ANS:
MSC: Skill
1  64x 2
PTS: 1
DIF: Medium
REF: 5.6.27
OBJ: Convert an inverse trigonometric expression to an algebraic expression
MSC: Skill
NOT: Section 5.6
18. ANS:
ÁÊ 4x ˜ˆ
1
arcsin ÁÁÁÁ ˜˜˜˜  C
4
Ë 3 ¯
PTS: 1
DIF: Medium
REF: 5.7.1
OBJ: Evaluate the indefinite integral involving an inverse trigonometric function
MSC: Skill
NOT: Section 5.7
3
ID: A
19. ANS:
dy
x

dx x 2  11
PTS: 1
DIF: Medium
REF: 5.1.54
OBJ: Differentiate a logarithmic function using the chain rule
NOT: Section 5.1
20. ANS:

PTS: 1
DIF: Medium
REF: 5.1.39
OBJ: Evaluate limits involving logarithmic functions
NOT: Section 5.1
21. ANS:
ÁÊÁ 5
˜ˆ
ÁÁ ,10ln 5 ˜˜˜
Á6
6 ˜¯
Ë
PTS: 1
DIF: Medium
REF: 5.1.93
OBJ: Identify all points of inflection for a function
NOT: Section 5.1
22. ANS:
MSC: Skill
MSC: Skill
MSC: Skill
1
f 1 (x )  (x  7 ) 3
PTS: 1
MSC: Skill
23. ANS:

DIF: Medium
NOT: Section 5.3
REF: 5.3.26a
OBJ: Construct the inverse of a function
1
x 2  9x  18
dx  x 2  12x  54ln x  3   C
2
x3
PTS: 1
DIF: Difficult
REF: 5.2.15
OBJ: Evaluate the indefinite integral of a function involving logarithms
MSC: Skill
NOT: Section 5.2
24. ANS:
1 
ln  sin(14 )   C
14
PTS: 1
DIF: Medium
REF: 5.2.37
OBJ: Evaluate the indefinite integral of a function involving logarithms
MSC: Skill
NOT: Section 5.2
25. ANS:
x 2 e x (x  3 )
PTS: 1
DIF: Medium
REF: 5.4.47
OBJ: Differentiate an exponential function using the chain rule and product rule
MSC: Skill
NOT: Section 5.4
4
ID: A
26. ANS:
5x 5x (lnx  1 )
PTS: 1
DIF: Medium
REF: 5.5.68
OBJ: Differentiate a function using logarithmic differentiation
NOT: Section 5.5
27. ANS:
ÊÁ
ˆ˜
x
ÁÁÁ x  4 ˜˜˜
dx  4 ln ÁÁ
˜ 2 x C
ÁÁ x  4 ˜˜˜
x  16
Ë
¯
MSC: Skill

PTS: 1
DIF: Medium
REF: 5.2.63
OBJ: Evaluate the definite integral of a function using a computer algebra system
MSC: Skill
NOT: Section 5.2
28. ANS:
15x  28
(3x  2)
3
PTS: 1
DIF: Medium
REF: 5.1.106
OBJ: Differentiate a function using logarithmic differentiation
NOT: Section 5.1
29. ANS:
13

36
MSC: Skill
PTS: 1
DIF: Easy
REF: 5.7.28
OBJ: Evaluate a definite integral involving inverse trigonometric functions
MSC: Skill
NOT: Section 5.7
5