Calculus 5th edition


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  • Chapter 1: Functions and Models
    • 1.1 Four Ways to Represent a Function (21)
    • 1.2 Mathematical Models: A Catalog of Essential Functions (6)
    • 1.3 New Functions from Old Functions (17)
    • 1.4 Graphing Calculators and Computers (7)

  • Chapter 2: Limits and Rates of Change
    • 2.1 The Tangent and Velocity Problems (4)
    • 2.2 The Limit of a Function (11)
    • 2.3 Calculating Limits Using the Limit Laws (19)
    • 2.4 The Precise Definition of a Limit (5)
    • 2.5 Continuity (8)
    • 2.6 Tangents, Velocities, and Other Rates of Change (10)

  • Chapter 3: Derivatives
    • 3.1 Derivatives (13)
    • 3.2 The Dericative as a Function (10)
    • 3.3 Differentiation Formulas (35)
    • 3.4 Rates of Change in the Natural and Social Sciences (10)
    • 3.5 Derivatives of Trigonometric Functions (21)
    • 3.6 The Chain Rule (33)
    • 3.7 Implicit Differentiation (20)
    • 3.8 Higher Derivatives (25)
    • 3.9 Related Rates (21)
    • 3.10 Linear Approximations and Differentials (17)

  • Chapter 4: Applications of Differentiation
    • 4.1 Maximum and Minimum Values (24)
    • 4.2 The Mean Value Theorem (3)
    • 4.3 How Derivatives Affect the Shape of a Graph (18)
    • 4.4 Limits at Infinity; Horizontal Asymptotes (21)
    • 4.5 Summary of Curve Sketching (2)
    • 4.6 Graphing with Calculus and Calculators (2)
    • 4.7 Optimization Problems (27)
    • 4.8 Applications to Business and Economics (9)
    • 4.9 Newton's Method (14)
    • 4.10 Antiderivatives (30)

  • Chapter 5: Integrals
    • 5.1 Areas and Distances (8)
    • 5.2 The Definite Integral (21)
    • 5.3 The Fundamental Theorem of Calculus (31)
    • 5.4 Indefinite Integrals and the Net Change Theorem (8)
    • 5.5 The Substitution Rule (35)

  • Chapter 6: Applications of Integration
    • 6.1 Areas between Curves (18)
    • 6.2 Volumes (30)
    • 6.3 Volumes by Cylindrical Shells (19)
    • 6.4 Work (13)
    • 6.5 Average Value of a Function (10)

  • Chapter 7: Inverse Functions
    • 7.1 Inverse Functions (10)
    • 7.2 Exponential Functions and Their Derivatives (8)
    • 7.3 Logarithmic Functions (10)
    • 7.4 Derivatives of Logarithmic Functions (8)
    • 7.5 Inverse Trigonometric Functions
    • 7.6 Hyperbolic Functions
    • 7.7 Indeterminate Forms and L'Hospital's Rule (15)

  • Chapter 8: Techniques of Integration
    • 8.1 Integration by Parts (21)
    • 8.2 Trigonometric Integrals (15)
    • 8.3 Trignonometric Substitution (6)
    • 8.4 Integration of Rational Functions by Partial Fractions (10)
    • 8.5 Strategy for Integration (11)
    • 8.6 Integration Using Tables and Computer Algebra Systems (6)
    • 8.7 Approximate Integration (10)
    • 8.8 Improper Integrals (13)

  • Chapter 9: Further Applications of Integration
    • 9.1 Arc Length (3)
    • 9.2 Area of a Surface of Revolution
    • 9.3 Applications to Physics and Engineering (3)
    • 9.4 Applications to Economics and Biology (3)
    • 9.5 Probability (2)

  • Chapter 10: Differential Equations
    • 10.1 Modeling with Differential Equations (3)
    • 10.2 Direction Fields and Euler's Method (4)
    • 10.3 Separable Equations (6)
    • 10.4 Exponential Growth and Decay (3)
    • 10.5 The Logistic Equation (2)
    • 10.6 Linear Equations
    • 10.7 Predator-Prey Systems (1)

  • Chapter 11: Parametric Equations and Polar Coordinates
    • 11.1 Curves Defined by Parametric Equations (6)
    • 11.2 Calculus with Parametric Curves (4)
    • 11.3 Polar Coordinates
    • 11.4 Areas and Lengths in Polar Coordinates (2)
    • 11.5 Conic Sections
    • 11.6 Conic Sections in Polar Coordinates

  • Chapter 12: Infinite Sequences and Series
    • 12.1 Sequences (8)
    • 12.2 Series (10)
    • 12.3 The Integral Test and Estimates of Sums (6)
    • 12.4 The Comparison Tests (16)
    • 12.5 Alternating Series (14)
    • 12.6 Absolute Convergence and the Ratio and Root Tests (5)
    • 12.7 Strategy for Testing Series (19)
    • 12.8 Power Series (6)
    • 12.9 Representations of Functions as Power Series (7)
    • 12.10 Taylor and Maclaurin Series (8)
    • 12.11 The Binomial Series (3)
    • 12.12 Applications of Taylor Polynomials (4)

  • Chapter 13: Vectors and the Geometry of Space
    • 13.1 Three-Dimensional Coordinate Systems (4)
    • 13.2 Vectors (4)
    • 13.3 The Dot Product (7)
    • 13.4 The Cross Product (6)
    • 13.5 Equations of Lines and Planes (8)
    • 13.6 Cylinders and Quadric Surfaces (1)
    • 13.7 Cylindrical and Spherical Coordinates (1)

  • Chapter 14: Vector Functions
    • 14.1 Vector Functions and Space Curves (4)
    • 14.2 Derivatives and Integrals of Vector Functions (5)
    • 14.3 Arc Length and Curvature (7)
    • 14.4 Motion in Space: Velocity and Acceleration (3)

  • Chapter 15: Partial Derivatives
    • 15.1 Functions of Several Variables (5)
    • 15.2 Limits and Continuity (5)
    • 15.3 Partial Derivatives (10)
    • 15.4 Tangent Planes and Linear Approximations (5)
    • 15.5 The Chain Rule (6)
    • 15.6 Directional Derivatives and the Gradient Vector (7)
    • 15.7 Maximum and Minimum Values (6)
    • 15.8 Lagrange Multipliers (5)

  • Chapter 16: Multiple Integrals
    • 16.1 Double Integrals over Rectangles (2)
    • 16.2 Iterated Integrals (5)
    • 16.3 Double Integrals over General Regions (7)
    • 16.4 Double Integrals in Polar Coordinates (4)
    • 16.5 Applications of Double Integrals (3)
    • 16.6 Surface Area (3)
    • 16.7 Triple Integrals (6)
    • 16.8 Triple Integrals in Cylindrical and Spherical Coordinates (5)
    • 16.9 Change of Variables in Multiple Integrals (2)

  • Chapter 17: Vector Calculus
    • 17.1 Vector Fields (6)
    • 17.2 Line Integrals (6)
    • 17.3 The Fundamental Theorem for Line Integrals (7)
    • 17.4 Green's Theorem (2)
    • 17.5 Curl and Divergence (3)
    • 17.6 Parametric Surfaces and Their Areas (4)
    • 17.7 Surface Integrals (7)
    • 17.8 Stokes' Theorem (2)
    • 17.9 The Divergence Theorem (4)
    • 17.10 Summary

  • Chapter 18: Second-Order Differential Equations
    • 18.1 Second-Order Linear Equations
    • 18.2 Nonhomogeneous Linear Equations
    • 18.3 Applications of Second- Order Differential Equations
    • 18.4 Series Solutions

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Group Quantity Questions
Chapter 1: Functions and Models
1.1 21 002 006 008 010 018 020 022 024 026 030 038 042 044 046 048 050 052 058 062 064 066
1.2 6 002 004 010 012 014 018
1.3 17 002 006 026 032 036 038 040 042 044 046 048 050 052 054 058 062 064
1.4 7 002 004 022 024 026 032 034
Chapter 2: Limits and Rates of Change
2.1 4 002 004 006 008
2.2 11 004 006 008 016 018 024 026 028 030 032 034
2.3 19 002 012 014 016 018 020 022 024 026 028 030 036 040 041 042 044 046 048 058
2.4 5 002 004 006 008 014
2.5 8 002 004 008 032 036 038 040 058
2.6 10 008 010 012 014 018 020 022 024 026 028
Chapter 3: Derivatives
3.1 13 002 004 008 010 014 016 018 020 022 024 026 030 036
3.2 10 002 004 018 020 022 024 026 028 036 044
3.3 35 002 004 006 008 010 012 014 016 018 020 023 024 026 028 030 032 034 035 036 038 040 042 046 052 054 056 058 060 062 064 068 070 072 076 084
3.4 10 002 004 006 008 010 018 020 022 026 034
3.5 21 002 003 004 006 008 010 012 014 016 022 024 026 030 032 034 036 038 040 042 044 046
3.6 33 002 004 006 008 010 012 014 016 018 020 022 024 025 026 028 030 032 034 036 038 040 042 044 046 048 052 054 056 058 060 064 066 074
3.7 20 002 004 006 008 010 012 014 016 018 020 022 024 025 026 028 030 032 044 052 053
3.8 25 002 004 006 008 010 012 014 016 018 020 024 026 028 030 032 034 036 040 042 044 046 048 050 054 056
3.9 21 002 004 006 008 009 010 012 014 016 018 019 020 022 024 026 028 030 032 034 036 038
3.10 17 002 004 006 008 012 014 016 018 020 022 024 026 032 034 036 040 042
Chapter 4: Applications of Differentiation
4.1 24 004 006 016 018 020 022 024 026 028 030 032 034 036 038 040 042 044 046 048 050 052 054 056 058
4.2 3 008 012 014
4.3 18 002 006 008 010 012 014 016 028 030 032 034 036 038 040 046 052 056 62
4.4 21 002 004 010 011 012 014 016 017 018 020 022 024 026 028 029 030 032 036 038 040 042
4.5 2 044 046
4.6 2 016 018
4.7 27 002 004 006 008 010 012 016 017 018 020 022 024 026 027 030 034 036 040 042 044 046 048 050 054 056 058 062
4.8 9 006 008 010 012 014 016 018 020 022
4.9 14 006 008 012 014 016 018 020 022 024 026 030 034 036 038
4.10 30 002 004 006 008 010 012 013 014 016 018 020 022 024 026 028 030 032 034 036 038 040 054 056 062 064 066 067 068 070 072
Chapter 5: Integrals
5.1 8 002 004 008 014 016 018 020 022
5.2 21 004 006 008 010 012 018 022 024 030 032 034 036 038 042 048 049 050 056 058 060 068
5.3 31 002 004 008 010 012 014 016 018 020 022 023 024 026 028 029 030 032 034 036 040 044 046 048 050 052 054 058 060 064 066 068
5.4 8 006 009 014 017 018 020 021 022 025 026 027 028 030 032 033 034 035 040 043 044 046 048 053 054 055 056 058 059 060 062 066 068
5.5 35 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 034 036 038 040 042 044 046 048 050 052 054 058 060 062 070 072 074 075 076 078
Chapter 6: Applications of Integration
6.1 18 002 004 006 009 012 014 024 028 032 034 036 040 041 042 044 046 048 052
6.2 30 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 042 044 046 048 050 052 054 056 058 060 064 066 068 070
6.3 19 004 006 010 012 012.alt 014 014.alt 016 018 020 022 028 030 032 034 036 038 040 042
6.4 13 002 004 006 008 010 012 014 016 018 020 022 024 030
6.5 10 002 004 006 008 010 012 014 016 018 022
Chapter 7: Inverse Functions
7.1 10 004 006 008 010 011 016 018 026 028 029
7.2 8 013 018 020 030 036 038 044 062
7.3 10 006 008 018 030 033 044 050 052 068 070
7.4 8 002 006 012 022 026 036 046 058
7.7 15 002 004 008 010 018 023 036 038 046 048 054 056 060 080 091
Chapter 8: Techniques of Integration
8.1 21 002 003 004 006 007 008 010 012 014 016 018 020 022 024 026 028 030 032 036 038 060
8.2 15 001 003 004 007 009 011 012 019 022 030 036 046 056 060 064
8.3 6 003 004 007 013 020 025
8.4 10 008 012 020 028 036 038 040 048 060 068
8.5 11 002 008 016 024 032 040 048 056 064 072 080
8.6 6 006 007 011 015 017 026
8.7 10 002 004 008 014 020 022 032 034 036 040
8.8 13 002 006 008 012 018 019 024 028 042 044 050 052 054
Chapter 9: Further Applications of Integration
9.1 3 004 022 034
9.3 3 012 022 024
9.4 3 002 010 012
9.5 2 008 012
Chapter 10: Differential Equations
10.1 3 004 010 012
10.2 4 004 006 022 024
10.3 6 010 014 016 028 036 040
10.4 3 002 008 012
10.5 2 004 008
10.7 1 008
Chapter 11: Parametric Equations and Polar Coordinates
11.1 6 012 016 020 022 024 040
11.2 4 006 012 033 044
11.4 2 020 032
Chapter 12: Infinite Sequences and Series
12.1 8 012 016 018 020 026 032 040 056
12.2 10 014 016 020 022 026 027 042 050 062 068
12.3 6 002 004 013 020 023 032
12.4 16 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 036
12.5 14 002 004 006 008 010 012 014 016 018 020 024 026 028 030
12.6 5 002 008 014 030 032
12.7 19 002 004 006 008 010 012 014 016 018 020 022 024 026 028 030 032 034 036 038
12.8 6 004 010 016 030 036 040
12.9 7 004 006 008 016 018 024 028
12.10 8 012 038 044 046 048 056 058 060
12.11 3 004 016 018
12.12 4 010 014 026 030
Chapter 13: Vectors and the Geometry of Space
13.1 4 004 010 036 042
13.2 4 004 018 028 034
13.3 7 002 004 006 012 018 046 048
13.4 6 010 012 024 030 032 036
13.5 8 008 020 024 030 032 036 038 072
13.6 1 046
13.7 1 056
Chapter 14: Vector Functions
14.1 4 006 020 022 024
14.2 5 010 022 024 026 032
14.3 7 002 004 009 016 020 022 026
14.4 3 010 026 028
Chapter 15: Partial Derivatives
15.1 5 002 010 054 056 058
15.2 5 006 008 014 018 038
15.3 10 006 008 014 018 036 038 042 048 066 090
15.4 5 004 006 019 032 034
15.5 6 009 014 022 032 038 040
15.6 7 004 018 020 024 025 030 034
15.7 6 010 028 030 032 038 042
15.8 5 004 006 008 018 038
Chapter 16: Multiple Integrals
16.1 2 002 006
16.2 5 004 006 012 026 028
16.3 7 002 004 008 018 026 044 056
16.4 4 014 022 024 030
16.5 3 002 010 014
16.6 3 002 008 024
16.7 6 004 008 012 019 038 046
16.8 5 002 004 008 013 020
16.9 2 002 006
Chapter 17: Vector Calculus
17.1 6 016 018 022 024 030 032
17.2 6 002 010 018 020 032 034
17.3 7 002 004 006 008 010 014 016
17.4 2 008 018
17.5 3 003 006 016
17.6 4 012 014 016 022
17.7 7 006 010 012 014 022 024 044
17.8 2 008 010
17.9 4 004 006 014 020
Total 1124 (24)