Calculus: Early Transcendental Functions L
k k k k
ectureNotes for Calculus 101
k k k k
Feras Awad Mahmoud
k k
Last Updated: August 2, 2012
k k k k
1
,2
Ferask Awadk Mahmoudk Departm
entk of k Basick ScienceskPhiladelphi
ak Universityk JORDAN k 19392
TEXTBOOK:
Thisk bookk isk stronglyk recommendedk fork Calculusk 101k ask wellk ask
— kofkthe k five k cha
ak reference ktext kfork Calculusk 102.k The k pdfksoft k copy
pterskremain k available kfork free k download.
TYPESETTING:
The kentire k document k wask writtenkink LaTeX,k implementedk fork Wi
ndowsk usingkthek MiKTeX k 2.9k distribution.k Ask forkthe ktext keditork o
fkmykchoice,k Ik fancyk WinEdt k6.0.
MORALk SUPPORT:
Myk wife k hask hadk ak verykinstrumental k role kink providingk moral k su
pport.k Thank k Godk fork herk patience,k understanding,k encour-
k agement,k and k prayers k throughout k the k longk process k ofk writingk an
dkediting.
⃝ ck2012k Ferask Awadk Mahmoud.k AllkRightskReserved.
www.philadelphia.edu.jo/academics/fawad
, Contents
Contents 3
1 Functions 5
1.1 Introduction ......................................................................................... 5
1.2 Essentialk Functions .............................................................................. 9
1.3 Combinationsk ofk Functions ................................................................26
1.4 InversekFunctions ................................................................................30
1.5 Hyperbolick Functions..........................................................................53
2 Limitsk andk Continuity 57
2.1 Ank Introductionk tok Limits ..................................................................57
2.2 Calculating k Limitsk using k thek Limitk Laws .........................................64
2.3 Limitskat kInfinity kand k Infinite kLimits ................................................73
2.4 LimitskInvolving k(sinkθ)k/θ ..................................................................86
2.5 Continuousk Functions .........................................................................89
3 Thek Derivative 97
3.1 Thek Derivativek as k a k Function .............................................................97
3.2 Differentiationk Rulesk andk Higher k Derivatives .................................103
3.3 Thek Chain k Rule.................................................................................113
3.4 Implicitk Differentiation ....................................................................119
3.5 Tangentk Line .....................................................................................122
4 Applicationsk of k Differentiation 127
3
, 2
4.1 Indeterminatek Formsk andk L ’Hôspital’s k Rule..................................127
4.2 Thek Meank Valuek Theorem ..............................................................134
4.3 Extremek Valuesk ofk Functions ..........................................................139
4.4 Monotonick Functions .......................................................................146
4.5 Concavityk andk Curvek Sketching......................................................151
5 Integration 159
5.1 Antiderivatives..................................................................................159
5.2 Indefinitek Integrals...........................................................................160
5.3 Integrationk byk Substitution .............................................................170
5.4 Thek Definitek Integral .......................................................................175
5.5 Thek Fundamentalk Theoremk ofk Calculus .........................................181
5.6 Areak Betweenk Twok Curves ..............................................................188
Ak Solving k Equationsk andk Inequalities 195
B Absolute k Value 207
C Equati on k of k Line 211
D Final k Answer sk of k Exercises 217
k k k k
ectureNotes for Calculus 101
k k k k
Feras Awad Mahmoud
k k
Last Updated: August 2, 2012
k k k k
1
,2
Ferask Awadk Mahmoudk Departm
entk of k Basick ScienceskPhiladelphi
ak Universityk JORDAN k 19392
TEXTBOOK:
Thisk bookk isk stronglyk recommendedk fork Calculusk 101k ask wellk ask
— kofkthe k five k cha
ak reference ktext kfork Calculusk 102.k The k pdfksoft k copy
pterskremain k available kfork free k download.
TYPESETTING:
The kentire k document k wask writtenkink LaTeX,k implementedk fork Wi
ndowsk usingkthek MiKTeX k 2.9k distribution.k Ask forkthe ktext keditork o
fkmykchoice,k Ik fancyk WinEdt k6.0.
MORALk SUPPORT:
Myk wife k hask hadk ak verykinstrumental k role kink providingk moral k su
pport.k Thank k Godk fork herk patience,k understanding,k encour-
k agement,k and k prayers k throughout k the k longk process k ofk writingk an
dkediting.
⃝ ck2012k Ferask Awadk Mahmoud.k AllkRightskReserved.
www.philadelphia.edu.jo/academics/fawad
, Contents
Contents 3
1 Functions 5
1.1 Introduction ......................................................................................... 5
1.2 Essentialk Functions .............................................................................. 9
1.3 Combinationsk ofk Functions ................................................................26
1.4 InversekFunctions ................................................................................30
1.5 Hyperbolick Functions..........................................................................53
2 Limitsk andk Continuity 57
2.1 Ank Introductionk tok Limits ..................................................................57
2.2 Calculating k Limitsk using k thek Limitk Laws .........................................64
2.3 Limitskat kInfinity kand k Infinite kLimits ................................................73
2.4 LimitskInvolving k(sinkθ)k/θ ..................................................................86
2.5 Continuousk Functions .........................................................................89
3 Thek Derivative 97
3.1 Thek Derivativek as k a k Function .............................................................97
3.2 Differentiationk Rulesk andk Higher k Derivatives .................................103
3.3 Thek Chain k Rule.................................................................................113
3.4 Implicitk Differentiation ....................................................................119
3.5 Tangentk Line .....................................................................................122
4 Applicationsk of k Differentiation 127
3
, 2
4.1 Indeterminatek Formsk andk L ’Hôspital’s k Rule..................................127
4.2 Thek Meank Valuek Theorem ..............................................................134
4.3 Extremek Valuesk ofk Functions ..........................................................139
4.4 Monotonick Functions .......................................................................146
4.5 Concavityk andk Curvek Sketching......................................................151
5 Integration 159
5.1 Antiderivatives..................................................................................159
5.2 Indefinitek Integrals...........................................................................160
5.3 Integrationk byk Substitution .............................................................170
5.4 Thek Definitek Integral .......................................................................175
5.5 Thek Fundamentalk Theoremk ofk Calculus .........................................181
5.6 Areak Betweenk Twok Curves ..............................................................188
Ak Solving k Equationsk andk Inequalities 195
B Absolute k Value 207
C Equati on k of k Line 211
D Final k Answer sk of k Exercises 217
