Calculus Concepts and Applications 2nd edition

Paul A. Foerster
Publisher: Kendall Hunt

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• Chapter 1: Limits, Derivatives, Integrals, and Integrals
• 1.1: The Concept of Instantaneous Rate (2)
• 1.2: Rate of Change by Equation, Graph, or Table (15)
• 1.3: One Type of Integral of a Function (9)
• 1.4: Definite Integrals by Trapezoids, from Equations and Data (8)
• 1.5: Calculus Journal
• 1.6: Chapter Review and Test (9)

• Chapter 2: Properties of Limits
• 2.1: Numerical Approach to the Definition of Limit
• 2.2: Graphical and Algebraic Approaches to the Definition of Limit (14)
• 2.3: The Limit Theorem (12)
• 2.4: Continuity and Discontinuity (23)
• 2.5: Limits Involving Infinity (9)
• 2.6: The Intermediate Value Theorem and Its Consequences (10)
• 2.7: Chapter Review and Test (19)

• Chapter 3: Derivatives, Antiderivatives, and Indefinite Integrals
• 3.1: Graphical Interpretation of Derivative
• 3.2: Difference Quotients and One Definition of Derivative (13)
• 3.3: Derivative Functions, Numerically and Graphically (10)
• 3.4: Derivative of the Power Function and Another Definition of Derivative (20)
• 3.5: Displacement, Velocity, and Acceleration (6)
• 3.6: Introduction to Sine, Cosine, and Composite Functions (4)
• 3.7: Derivatives of Composite Functions—The Chain Rule (30)
• 3.8: Proof and Application of Sine and Cosine Derivatives (4)
• 3.9: Exponential and Logarithmic Functions (30)
• 3.10: Chapter Review and Test (30)

• Chapter 4: Products, Quotients, and Parametric Functions
• 4.1: Combinations of Two Functions
• 4.2: Derivative of a Product of Two Functions (18)
• 4.3: Derivative of a Quotient of Two Functions (17)
• 4.4: Derivatives of the Other Trigonometric Functions (18)
• 4.5: Derivatives of Inverse Trigonometric Functions (16)
• 4.6: Differentiability and Continuity (17)
• 4.7: Derivatives of a Parametric Function
• 4.8: Graphs and Derivatives of Implicit Relations (27)
• 4.9: Related Rates (12)
• 4.10: Chapter Review and Test (24)

• Chapter 5: Definite and Indefinite Integrals
• 5.1: A Definite Integral Problem
• 5.2: Linear Approximations and Differentials (22)
• 5.3: Formal Definition of Antiderivative and Indefinite Integral (37)
• 5.4: Riemann Sums and the Definition of Definite Integral (6)
• 5.5: The Mean Value Theorem and Rolle's Theorem (21)
• 5.6: The Fundamental Theorem of Calculus (4)
• 5.7: Definite Integral Properties and Practice (20)
• 5.8: Definite Integrals Applied to Area and Other Problems (16)
• 5.9: Volume of a Solid by Plane Slicing (20)
• 5.10: Definite Integrals Numerically by Grapher and by Simpson's Rule (8)
• 5.11: Chapter Review and Test (27)

• Chapter 6: The Calculus of Exponential and Logarithmic Functions
• 6.1: Integral of the Reciprocal Function: A Population Growth Problem
• 6.2: Antiderivative of the Reciprocal Function and Another Form of the Fundamental Theorem (33)
• 6.3: The Uniqueness Theorem and Properties of Logarithmic Functions (14)
• 6.4: The Number e, Exponential Functions, and Logarithmic Differentiation (34)
• 6.5: Limits of Indeterminate Forms: l'Hospital's Rule (19)
• 6.6: Derivative and Integral Practice for Transcendental Functions (90)
• 6.7: Chapter Review and Test (22)
• 6.8: Cumulative Review: Chapters 1–6

• Chapter 7: The Calculus of Growth and Decay
• 7.1: Direct Proportion Property of Exponential Functions
• 7.2: Exponential Growth and Decay (8)
• 7.3: Other Differential Equations for Real-World Applications (4)
• 7.4: Graphical Solution of Differential Equations by Using Slope Fields (13)
• 7.5: Numerical Solution of Differential Equations by Using Euler's Method (11)
• 7.6: The Logistic Function, and Predator-Prey Population Problems (11)
• 7.7: Chapter Review and Test (8)
• 7.8: Cumulative Review: Chapters 1–7

• Chapter 8: The Calculus of Plane and Solid Figures
• 8.1: Cubic Functions and Their Derivatives
• 8.2: Critical Points and Points of Inflection (28)
• 8.3: Maxima and Minima in Plane and Solid Figures (13)
• 8.4: Volume of a Solid of Revolution by Cylindrical Shells (9)
• 8.5: Length of a Plane Curve—Arc Length (14)
• 8.6: Area of a Surface of Revolution (8)
• 8.7: Lengths and Areas for Polar Coordinates (9)
• 8.8: Chapter Review and Test (29)

• Chapter 9: Algebraic Calculus Techniques for the Elementary Functions
• 9.1: Introduction to the Integral of a Product of Two Functions
• 9.2: Integration by Parts—A Way to Integrate Products (6)
• 9.3: Rapid Repeated Integration by Parts (26)
• 9.4: Reduction Formulas and Computer Algebra Systems (12)
• 9.5: Integrating Special Powers of Trigonometric Functions (18)
• 9.6: Integration by Trigonometric Substitution (25)
• 9.7: Integration of Rational Functions by Partial Fractions (13)
• 9.8: Integrals of the Inverse Trigonometric Functions (5)
• 9.9: Calculus of the Hyperbolic and Inverse Hyperbolic Functions (19)
• 9.10: Improper Integrals (14)
• 9.11: Miscellaneous Integrals and Derivatives (48)
• 9.12: Integrals in Journal
• 9.13: Chapter Review and Test (50)

• Chapter 10: The Calculus of Motion—Averages, Extremes, and Vectors
• 10.1: Introduction to Distance and Displacement for Motion Along a Line
• 10.2: Distance, Displacement, and Acceleration for Linear Motion (8)
• 10.3: Average Value Problems in Motion and Elsewhere (10)
• 10.4: Minimal Path Problems (7)
• 10.5: Maximum and Minimum Problems in Motion and Elsewhere (9)
• 10.6: Vector Functions for Motion in a Plane (9)
• 10.7: Chapter Review and Test (12)

• Chapter 11: The Calculus of Variable-Factor Products
• 11.1: Review of Work—Force Times Displacement
• 11.2: Work Done by a Variable Force (6)
• 11.3: Mass of a Variable-Density Object (7)
• 11.4: Moments, Centroids, Center of Mass, and the Theorem of Pappus (8)
• 11.5: Force Exerted by a Variable Pressure—Center of Pressure (4)
• 11.6: Other Variable-Factor Products (10)
• 11.7: Chapter Review and Test (8)

• Chapter 12: The Calculus of Functions Defined by Power Series
• 12.1: Introduction to Power Series
• 12.2: Geometric Sequences and Series as Mathematical Models (5)
• 12.3: Power Series for an Exponential Function (11)
• 12.4: Power Series for Other Elementary Functions (4)
• 12.5: Taylor and Maclaurin Series, and Operations on These Series (31)
• 12.6: Interval of Convergence for a Series—The Ratio Technique (16)
• 12.7: Convergence of Series at the Ends of the Convergence Interval (29)
• 12.8: Error Analysis for Series—The Lagrange Error Bound (10)
• 12.9: Chapter Review and Test (44)
• 12.10: Cumulative Reviews

Paul Foerster authored Calculus Concepts and Applications, 2nd edition, with the high school student in mind, but with all the content of a college-level course. This title follows the AP Calculus curriculum for both AB and BC levels. The WebAssign component for this text provides online versions of the exercises author Paul Foerster developed from his 50 years of classroom experience. Questions link directly to the eBook and supplemental material such as the Instructor Resource Book, the Instructor Solution Manual, the Teacher Edition, technology projects, word file test banks, and exploration worksheets are included.

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Question Group Key
C - Concept Problems
R - Review Problems
T - Chapter Test Problems

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Group Quantity Questions
Chapter 1: Limits, Derivatives, Integrals, and Integrals
1.1 2 001 002
1.2 15 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029
1.3 9 001 003 005 007 009 011 012 013 014
1.4 8 001 003 005 006 007 009 011 013
1.6 9 C.001 C.002 R.001 R.002a R.002b R.002c R.002d R.003 R.004
Chapter 2: Properties of Limits
2.2 14 001 003 005 007 009 011 013 015 017 019 021 023 025 027
2.3 12 001 003 005 007 009 011 013 015 017 019 021 023
2.4 23 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 039 041 043 045
2.5 9 001 003 005 007 009 011 012 013 014
2.6 10 001 002 003 004 005 009 010 011 012 014
2.7 19 C.001 C.002 R.001 R.002 R.003a R.003b R.003c R.004a R.004b R.004c R.004d R.005a R.005b R.005c R.005d R.005e R.006a R.006b R.006c
Chapter 3: Derivatives, Antiderivatives, and Indefinite Integrals
3.2 13 001 002 003 005 007 009 011 013 015 017 019a-c 019d-f 020
3.3 10 001 003 005 007 009 011 013 014 015 016
3.4 20 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 034 039 040
3.5 6 001 005 007 008 009 011
3.6 4 001 002 006 007
3.7 30 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030
3.8 4 001 003 007 013
3.9 30 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030
3.10 30 C.001 C.002 R.001 R.002 R.003a-c R.003d R.004a-b R.004c R.004d R.004f R.004g-h R.004i R.005a R.005b R.005c R.005d R.005e R.006 R.007a-b R.007c R.007d R.007e R.007f R.008a-b R.008c-d R.008e R.009a R.009b R.009c R.009d
Chapter 4: Products, Quotients, and Parametric Functions
4.2 18 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035
4.3 17 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 030 032
4.4 18 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035
4.5 16 001 003 005 007 009 011 013 014 015 016 017 019 021 023 025 029
4.6 17 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033
4.8 27 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027
4.9 12 001 002 003 004 005 006 007 008 009 010 011 012
4.10 24 C.001 R.001 R.002c R.002d R.003c R.003d R.003e-f R.004a R.004b R.004c R.004d R.005a R.005b R.006a R.006b R.006c R.006d R.007a R.007b R.007c R.008a R.008b R.008c R.009
Chapter 5: Definite and Indefinite Integrals
5.2 22 001 003 005 006 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 039 041
5.3 37 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037
5.4 6 001 003 005 007 009 011
5.5 21 001 002 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 034 039 040
5.6 4 001 007 008 009
5.7 20 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 038
5.8 16 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031
5.9 20 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 019 021 023
5.10 8 001 004 005 006 007 011 015 016
5.11 27 C.001 R.001 R.002a R.002b R.002c R.002d R.003 R.004 R.005a R.005b R.005c R.005d R.005f R.005g R.006a R.006b-d R.007a-b R.007c R.007d R.008a R.008b R.009a R.009b R.009c R.010a R.010b R.010c
Chapter 6: The Calculus of Exponential and Logarithmic Functions
6.2 33 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 039 041 043 045 047 049 051 053 055 057 059 060 061 062
6.3 14 001 003 005 009 011 013 015 017 019 021 023 025 027 029
6.4 34 001 002 003 004 005 006 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 039 041 043 045 047 049 051 053 055 057 059 061
6.5 19 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 036
6.6 90 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 048 049 050 051 052 053 054 055 056 057 058 059 060 061 062 063 064 065 066 067 068 069 070 071 072 073 074 075 076 077 078 079 080 081 082 083 084 085 086 087 088 089 090
6.7 22 C.005 C.006 R.001 R.002a R.002b R.002c R.002d R.002e R.002f R.003a R.003b R.003c R.004a R.004b R.004c R.004d R.004e R.004f R.005 R.006a R.006b R.006c
Chapter 7: The Calculus of Growth and Decay
7.2 8 001 002 003 004 005 006 008 009
7.3 4 001 004 005 007
7.4 13 001 002 003 004 005 006 007 008 009 010 011 012 014
7.5 11 001 002 003 004 005 006 007 008 009 010 011
7.6 11 001 002 003 009 011 013 017 018 019 021 023
7.7 8 R.001 R.002 R.003a-d R.003e R.004 R.005 R.006a-c R.006d-g
Chapter 8: The Calculus of Plane and Solid Figures
8.2 28 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 038 039 040 041 042 043 044 045 046
8.3 13 001 003 005 007 011 015 017 019 023 025 027 029 031
8.4 9 001 003 007 009 011 015 017 019 021
8.5 14 001 003 005 007 009 011 013 015 017 019 025 027 031 032
8.6 8 001 003 005 007 009 011 013 015
8.7 9 001 003 005 007 009 011 013 018 019
8.8 29 R.001 R.002a R.002b R.002c R.002d R.003a R.003b R.004a-b R.004c R.005a R.005b R.005c R.006a R.006b R.007 T.001 T.002 T.003 T.004 T.005 T.006 T.007 T.008 T.009 T.010 T.011 T.012 T.013 T.014
Chapter 9: Algebraic Calculus Techniques for the Elementary Functions
9.2 6 001 003 005 007 009 011
9.3 26 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037 039 041 043 044 045 047 049
9.4 12 001 003 005 007 009 011 013 015 017 019 020 021
9.5 18 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035
9.6 25 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 026
9.7 13 001 003 005 007 009 011 013 015 017 019 021 023 024
9.8 5 001 003 005 007 009
9.9 19 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 033 035 037
9.10 14 001 003 005 007 009 011 013 015 017 019 021 022 023 024
9.11 48 001 003 005 007 009 011 013 015 017 019 021 023 025 027 029 031 037 039 041 043 045 047 049 051 053 055 057 059 061 063 065 067 069 071 073 075 077 079 081 083 085 087 089 091 093 095 097 099
9.13 50 R.001 R.002 R.003a R.003b R.003c R.003d R.004a R.004b R.004c R.005a R.005b R.005c R.005d R.005e R.005f R.006a R.006b R.006c R.006d R.007a R.007b R.007c R.007d R.007e R.008a R.008b R.008c R.008d R.009a R.009b R.009c R.009d R.009e R.009f R.009g R.009h R.010a R.010b R.010c R.010d R.010e R.011a R.011b R.011c R.011d R.011e R.011f R.011g R.011h R.012
Chapter 10: The Calculus of Motion—Averages, Extremes, and Vectors
10.2 8 001 003 005 007 009 011 013 015
10.3 10 001 003 005 007 009 011 013 015 017 019
10.4 7 001 002 003 004 005 006 007
10.5 9 001 003 005 007 008 009 010 011 012
10.6 9 001 003 005 006 007 008 009 011 017
10.7 12 C.001 R.001 R.002a R.002b R.003a R.003b R.004a R.004b R.005a R.005b R.006a R.006b
Chapter 11: The Calculus of Variable-Factor Products
11.2 6 001 003 005 007 008 009
11.3 7 001 003 005 007 009 011 013
11.4 8 001 003 005 007 009 011 013 015
11.5 4 001 003 005 007
11.6 10 001 003 005 007 009 011 013 014 015 016
11.7 8 R.001 R.002a R.002b R.003 R.004a R.004b R.005 R.006
Chapter 12: The Calculus of Functions Defined by Power Series
12.2 5 001 003 005 007 009
12.3 11 001 002 003 004 005 006 007 008 009 010 011
12.4 4 001 003 005 007
12.5 31 001 002 003 004 005 006 007 008 009 011 013 015 016 017 018 019 020 021 022 023 024 025 027 029 031 033 035 037 039 040 041
12.6 16 001 003 005 007 009 011 013 015 017 019 021 022 023 024 025 026
12.7 29 001 002 003 005 007 008 010 011 012 013 015 017 019 021 023 025 027 029 031 033 034 035 036 037 039 041 043 045 047
12.8 10 001 003 005 007 009 011 013 015 017 019
12.9 44 R.001 R.002a R.002b R.003 R.004a R.004b R.004c R.004d R.005a-d R.005e R.005f R.005g R.006a-b R.006c R.006d R.006e R.007a-d R.007e R.007f R.007g R.007h-i R.007j R.007k R.008a R.008b R.008c R.008d R.008e R.008f T.001 T.002 T.003 T.004 T.005 T.006 T.007 T.008 T.009 T.010 T.011 T.012 T.013 T.014 T.015
Total 1468