Solution
Manual for
Applied
Calculus
7th Edition
Berresford
Rockett
,Contents
Diagnostic Test 1
Chapter 1 Functions 3
Chapter 2 Derivatives and Their Uses 41
Chapter 3 Further Applications of Derivatives 95
Chapter 4 Exponential and Logarithmic Functions 189
Chapter 5 Integration and Its Applications 222
Chapter 6 Integration Techniques 290
Chapter 7 Calculus of Several Variables 344
Chapter 8 Trigonometric Functions 415
Chapter 9 Differential Equations 454
Chapter 10 Sequences and Series 510
Chapter 11 Probability 552
Chapter Tests 595
Chapter Test Solutions 655
,DIAGNOSTIC g;TEST
Are g ; you g ; ready g ; to g ; study g ; calculus?
Algebra g;is g;the g;language g;in g;which g;we g;express g;the g;ideas g;of g;calculus. g ; Therefore, g;to
g;un- g;derstand g ; calculus g ; and g ; express g ; its g;ideas g ; with g;precision, g ; you g ; need g ; to g;know
g;some g;algebra.
If g;you g;are g;comfortable g;with g;the g;algebra g;covered g;in g;the g;following g;problems, g;you
g;are g;ready g;to g;begin g;your g;study g;of g;c alculus. g ; If g;not, g;turn g ; to g;the g;Algebra g;Appendix
g;beginning g;on g;page g;A.xxx g;and g;review g;the g;Complete g;Solutions g;to g;these g;problems,
g;and g;continue g;reading g ; the g ; other g ; parts g ; of g;the g;Appendix g ; that g ; cover g ; anything
g;that g ; you g ; do g ; not g ; know.
Problems Answers
1. True g ; or g;False? 12 g ; < 3
2. Express g ; g ; {x| 4 g;< g ; x 5} g ; in g ; interval g ; notation.
3. What g ; is g ; the g ; slope g ; of g;the g ; line g ; through g ; the g ; points g ; (6, 7) g;and g ; (9, g;8)?
4. On g ; the g ; line g ; y g;= g;3x g;+ g;4, g ; what g ; value g ; of y g;corresponds g ; to x g ; = g ; 2?
5. Which g ; sketch g ; shows g;the g;graph g ; of g;the g;line g ; y g;= g;2x 1?
✓ px◆ g ; 2
y2
True g ; or g;False? =
y x
6.
7. Find g ; the g ; zeros g ; of g;the g ; function g ; g; f(x) g;= g ; 9x2 6x 1
8. Expand g ; and g ; simplify g ; x(8 x) (3x g ; + g;7).
x2 3x g;+ g;2
9. What g;is g ;the g;domain g;of g; x3 g ; + g;x2 6x
g ; f(x) g;= ?
g;
f(x g;+ g;h) f(x)
10. For g ; g ; f(x) g ; = g ; x2 5x, g ; find g;the g;di↵erence .
g ; quotient
h
g;
, Diagnostic g ; Test g ; (in g ; Front g ; Matter)
Manual for
Applied
Calculus
7th Edition
Berresford
Rockett
,Contents
Diagnostic Test 1
Chapter 1 Functions 3
Chapter 2 Derivatives and Their Uses 41
Chapter 3 Further Applications of Derivatives 95
Chapter 4 Exponential and Logarithmic Functions 189
Chapter 5 Integration and Its Applications 222
Chapter 6 Integration Techniques 290
Chapter 7 Calculus of Several Variables 344
Chapter 8 Trigonometric Functions 415
Chapter 9 Differential Equations 454
Chapter 10 Sequences and Series 510
Chapter 11 Probability 552
Chapter Tests 595
Chapter Test Solutions 655
,DIAGNOSTIC g;TEST
Are g ; you g ; ready g ; to g ; study g ; calculus?
Algebra g;is g;the g;language g;in g;which g;we g;express g;the g;ideas g;of g;calculus. g ; Therefore, g;to
g;un- g;derstand g ; calculus g ; and g ; express g ; its g;ideas g ; with g;precision, g ; you g ; need g ; to g;know
g;some g;algebra.
If g;you g;are g;comfortable g;with g;the g;algebra g;covered g;in g;the g;following g;problems, g;you
g;are g;ready g;to g;begin g;your g;study g;of g;c alculus. g ; If g;not, g;turn g ; to g;the g;Algebra g;Appendix
g;beginning g;on g;page g;A.xxx g;and g;review g;the g;Complete g;Solutions g;to g;these g;problems,
g;and g;continue g;reading g ; the g ; other g ; parts g ; of g;the g;Appendix g ; that g ; cover g ; anything
g;that g ; you g ; do g ; not g ; know.
Problems Answers
1. True g ; or g;False? 12 g ; < 3
2. Express g ; g ; {x| 4 g;< g ; x 5} g ; in g ; interval g ; notation.
3. What g ; is g ; the g ; slope g ; of g;the g ; line g ; through g ; the g ; points g ; (6, 7) g;and g ; (9, g;8)?
4. On g ; the g ; line g ; y g;= g;3x g;+ g;4, g ; what g ; value g ; of y g;corresponds g ; to x g ; = g ; 2?
5. Which g ; sketch g ; shows g;the g;graph g ; of g;the g;line g ; y g;= g;2x 1?
✓ px◆ g ; 2
y2
True g ; or g;False? =
y x
6.
7. Find g ; the g ; zeros g ; of g;the g ; function g ; g; f(x) g;= g ; 9x2 6x 1
8. Expand g ; and g ; simplify g ; x(8 x) (3x g ; + g;7).
x2 3x g;+ g;2
9. What g;is g ;the g;domain g;of g; x3 g ; + g;x2 6x
g ; f(x) g;= ?
g;
f(x g;+ g;h) f(x)
10. For g ; g ; f(x) g ; = g ; x2 5x, g ; find g;the g;di↵erence .
g ; quotient
h
g;
, Diagnostic g ; Test g ; (in g ; Front g ; Matter)
