# Mathematical Applications for the Management, Life, and Social Sciences 12th edition

Ronald J. Harshbarger and James J. Reynolds
Publisher: Cengage Learning

## eBook

Access is contingent on use of this textbook in the instructor's classroom.

Higher Education Single Term \$90.00
High School \$35.00

Online price per student per course or lab, bookstore price varies. Access cards can be packaged with most any textbook, please see your textbook rep or contact WebAssign

• Chapter 1: Linear Equations and Functions
• 1.1: Solutions of Linear Equations and Inequalities in One Variable (34)
• 1.2: Functions (26)
• 1.3: Linear Functions (37)
• 1.4: Graphs and Graphing Utilities (13)
• 1.5: Solutions of Systems of Linear Equations (36)
• 1.6: Applications of Functions in Business and Economics (39)
• 1: Review Exercises
• 1: Chapter Test

• Chapter 2: Quadratic and Other Special Functions
• 2.2: Quadratic Functions: Parabolas (27)
• 2.4: Special Functions and Their Graphs (23)
• 2.5: Modeling; Fitting Curves to Data with Graphing Utilities (15)
• 2: Review Exercises
• 2: Chapter Test

• Chapter 3: Matrices
• 3.1: Matrices (21)
• 3.2: Multiplication of Matrices (31)
• 3.3: Gauss-Jordan Elimination: Solving Systems of Equations (33)
• 3.4: Inverse of a Square Matrix; Matrix Equations (30)
• 3.5: Applications of Matrices: Leontief Input-Output Models (18)
• 3: Review Exercises
• 3: Chapter Test

• Chapter 4: Inequalities and Linear Programming
• 4.1: Linear Inequalities in Two Variables (23)
• 4.2: Linear Programming: Graphical Methods (24)
• 4.3: The Simplex Method: Maximization (30)
• 4.4: The Simplex Method: Duality and Minimization (18)
• 4.5: The Simplex Method with Mixed Constraints (25)
• 4: Review Exercises
• 4: Chapter Test

• Chapter 5: Exponential and Logarithmic Functions
• 5.1: Exponential Functions (18)
• 5.2: Logarithmic Functions and Their Properties (34)
• 5.3: Equations and Applications with Exponential and Logarithmic Functions (28)
• 5: Review Exercises
• 5: Chapter Test

• Chapter 6: Mathematics of Finance
• 6.1: Simple Interest; Sequences (27)
• 6.2: Compound Interest; Geometric Sequences (39)
• 6.3: Future Values of Annuities (25)
• 6.4: Present Values of Annuities (29)
• 6.5: Loans and Amortization (19)
• 6: Review Exercises
• 6: Chapter Test

• Chapter 7: Introduction to Probability
• 7.1: Probability; Odds (37)
• 7.2: Unions and Intersections of Events: One-Trial Experiments (24)
• 7.3: Conditional Probability: The Product Rule (35)
• 7.4: Probability Trees and Bayes' Formula (17)
• 7.5: Counting: Permutations and Combinations (29)
• 7.6: Permutations, Combinations, and Probability (26)
• 7.7: Markov Chains (25)
• 7: Review Exercises
• 7: Chapter Test

• Chapter 8: Further Topics in Probability; Data Description
• 8.1: Binomial Probability Experiments (16)
• 8.2: Data Description (30)
• 8.3: Discrete Probability Distributions; The Binomial Distribution (27)
• 8.4: Normal Probability Distribution (29)
• 8.5: The Normal Curve Approximation to the Binomial Distribution (21)
• 8: Review Exercises
• 8: Chapter Test

• Chapter 9: Derivatives
• 9.1: Limits (37)
• 9.2: Continuous Functions; Limits at Infinity (28)
• 9.3: Rates of Change and Derivatives (27)
• 9.4: Derivative Formulas (33)
• 9.5: The Product Rule and the Quotient Rule (31)
• 9.6: The Chain Rule and the Power Rule (37)
• 9.7: Using Derivative Formulas (27)
• 9.8: Higher-Order Derivatives (25)
• 9.9: Applications: Marginals and Derivatives (20)
• 9: Review Exercises
• 9: Chapter Test

• Chapter 10: Applications of Derivatives
• 10.1: Relative Maxima and Minima: Curve Sketching (32)
• 10.2: Concavity; Points of Inflection (26)
• 10.3: Optimization in Business and Economics (26)
• 10.4: Applications of Maxima and Minima (18)
• 10.5: Rational Functions: More Curve Sketching (24)
• 10: Review Exercises
• 10: Chapter Test

• Chapter 11: Derivatives Continued
• 11.1: Derivatives of Logarithmic Functions (32)
• 11.2: Derivatives of Exponential Functions (32)
• 11.3: Implicit Differentiation (35)
• 11.4: Related Rates (22)
• 11.5: Applications in Business and Economics (14)
• 11: Review Exercises
• 11: Chapter Test

• Chapter 12: Indefinite Integrals
• 12.1: Indefinite Integrals (32)
• 12.2: The Power Rule (27)
• 12.3: Integrals Involving Exponential and Logarithmic Functions (28)
• 12.4: Applications of the Indefinite Integral in Business and Economics (19)
• 12.5: Differential Equations (31)
• 12: Review Exercises
• 12: Chapter Test

• Chapter 13: Definite Integrals: Techniques of Integration
• 13.1: Area Under a Curve (22)
• 13.2: The Definite Integral: The Fundamental Theorem of Calculus (34)
• 13.3: Area Between Two Curves (26)
• 13.4: Applications of Definite Integrals in Business and Economics (23)
• 13.5: Using Tables of Integrals (30)
• 13.6: Integration by Parts (22)
• 13.7: Improper Integrals and Their Applications (28)
• 13.8: Numerical Integration Methods: The Trapezoidal Rule and Simpson's Rule (20)
• 13: Review Exercises
• 13: Chapter Test

• Chapter 14: Functions of Two or More Variables
• 14.1: Functions of Two or More Variables (22)
• 14.2: Partial Differentiation (33)
• 14.3: Applications of Functions of Two Variables in Business and Economics (15)
• 14.4: Maxima and Minima (18)
• 14.5: Maxima and Minima of Functions Subject to Constraints: Lagrange Multipliers (18)
• 14: Review Exercises
• 14: Chapter Test

• Chapter 0: Algebraic Concepts
• 0.1: Sets (27)
• 0.2: The Real Numbers (24)
• 0.3: Integral Exponents (21)
• 0.4: Radicals and Rational Exponents (28)
• 0.5: Operations with Algebraic Expressions (28)
• 0.6: Factoring (23)
• 0.7: Algebraic Fractions (25)
• 0: Review Exercises
• 0: Chapter Test

Mathematical Applications for the Management, Life, and Social Sciences, 12th edition, engages students with its concept-based approach, multiple presentation methods, and relevant applications throughout. Intended for two-semester applied calculus or combined finite mathematics and applied calculus courses, the book places concepts in real-life contexts to help students strengthen their understanding. A focus on modeling (with modeling problems clearly labeled in the examples and problems, so they can be treated as optional) and flexible content organization accommodate different teaching approaches, enabling instructors to decide the order in which topics are presented and the degree to which they are emphasized.

The WebAssign enhancement to this textbook, which includes an interactive eBook, is a fully customizable online solution that empowers students to learn, not just do homework. Insightful tools save time and highlight exactly where students are struggling. Students get an engaging experience, instant feedback, and better outcomes. A total win-win!

Features
• Read It links under each question quickly jump to the corresponding section of a complete, interactive eBook that lets students highlight and take notes as they read.
• Watch It links provide step-by-step instruction with short, engaging videos that are ideal for visual learners.
• Master It Tutorials (MI) show how to solve a similar problem in multiple steps by providing direction along with derivation so students understand the concepts and reasoning behind the problem solving.
• Course Packs with ready-to-use assignments built by subject matter experts specifically for this textbook are designed to save you time, and can be easily customized to meet your teaching goals.
• A Personal Study Plan lets your students use chapter and section assessments to gauge their mastery of the material and generate individualized study plans that include various online, interactive multimedia resources.
• Students can Talk to a Tutor for additional assistance through a link at the assignment level.
• Select questions contain detailed solutions to the problem, available to students at your discretion.
• Lecture videos are available as a textbook resource.
• Select projects are now available in WebAssign, making the task of collecting and grading projects easier.
Use the Textbook Edition Upgrade Tool to automatically update all of your assignments from the previous edition to corresponding questions in this textbook.

## Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

##### Question Group Key
MI - Master It Tutorial
MI.SA - Stand Alone Master It

##### Question Availability Color Key
BLACK questions are available now
GRAY questions are under development

Group Quantity Questions
Chapter 0: Algebraic Concepts
0.1 27 001 004 006 010 012 014 018 019 020 024 026 028 030 032 034 035.MI 035.MI.SA 036 038 040 045.MI 045.MI.SA 048 049 051 052 054
0.2 24 001 003 005 008 010 012 013 016.MI 016.MI.SA 018 022.MI 022.MI.SA 024 029 034 036 037.MI 037.MI.SA 039 040 042 044 051 501.XP
0.3 21 010 012 016.MI 016.MI.SA 021 024 026 029 032.MI 032.MI.SA 040 042.MI 042.MI.SA 044 048 051 054 056 057 061 067
0.4 28 006 008 010 013 016 017.MI 017.MI.SA 022 026 031 034 037.MI 037.MI.SA 041 044 045 049 052 054 056 058 060 063 064 066 069 072 073
0.5 28 002 004 007 010 014 015.MI 015.MI.SA 016 018 022 025 028 032 036 040 047 050 054 056 059.MI 059.MI.SA 061.MI 061.MI.SA 070 071 072 073 074
0.6 23 004 005.MI 005.MI.SA 007 010 014 018 019.MI 019.MI.SA 022 024 028 032 036 040 046 052.MI 052.MI.SA 058 060 061 062 063
0.7 25 001 004 005 007 009 012 014 017.MI 017.MI.SA 023 026 028 033 035.MI 035.MI.SA 038 041 043 044 047.MI 047.MI.SA 051 054 055 058
Chapter 1: Linear Equations and Functions
1.1 34 003 005.MI 005.MI.SA 009 010 013 016 018.MI 018.MI.SA 019 021 023 027 029 031 033.MI 033.MI.SA 035 037 039 040 041 045 047 049 051.MI 051.MI.SA 056 057 059 061 062 068 501.XP
1.2 26 001 003 009 011 015 017 019 020 021 025.MI 025.MI.SA 027 029 033.MI 033.MI.SA 035 037.MI 037.MI.SA 044 047 049 050 051 052 053 054
1.3 37 001 003 005.MI 005.MI.SA 007 009 011 013 015.MI 015.MI.SA 017 019 021 023.MI 023.MI.SA 025 027.MI 027.MI.SA 029.MI 029.MI.SA 031 033 035.MI 035.MI.SA 037 041.MI 041.MI.SA 043 045.MI 045.MI.SA 047 049.MI 049.MI.SA 057 063 064 065
1.4 13 007 017.MI 017.MI.SA 029 031 035.MI 035.MI.SA 037 039 043 044 045 047
1.5 36 003.MI 003.MI.SA 005 007.MI 007.MI.SA 009 011 013.MI 013.MI.SA 015 017.MI 017.MI.SA 020.MI 020.MI.SA 022 023 025 027.MI 027.MI.SA 031 032 035.MI 035.MI.SA 037.MI 037.MI.SA 043.MI 043.MI.SA 044.MI 044.MI.SA 045 048.MI 048.MI.SA 051 501.XP 502.XP.MI 502.XP.MI.SA
1.6 39 001.MI 001.MI.SA 003 004.MI 004.MI.SA 007 008 009 011.MI 011.MI.SA 013 015 017.MI 017.MI.SA 019 021 023 026 027 031 033 035 036.MI 036.MI.SA 039 040 041 044.MI 044.MI.SA 045 047 049 050.MI 050.MI.SA 051 055 057 058.MI 058.MI.SA
Chapter 2: Quadratic and Other Special Functions
2.1 42 001.MI 001.MI.SA 003 005 007.MI 007.MI.SA 009 011 015.MI 015.MI.SA 017 021.MI 021.MI.SA 023 025 027 029.MI 029.MI.SA 033.MI 033.MI.SA 037 039 043.MI 043.MI.SA 045 047.MI 047.MI.SA 049.MI 049.MI.SA 051 053.MI 053.MI.SA 054.MI 054.MI.SA 055 057.MI 057.MI.SA 059 064.MI 064.MI.SA 066.MI 066.MI.SA
2.2 27 001 003 005 006 007.MI 007.MI.SA 009 011 012 013 015 017 021.MI 021.MI.SA 022 025 029 031 033 037.MI 037.MI.SA 039 041 043 044 045 048
2.3 21 001 003 004.MI 004.MI.SA 006 007 009 010 011 012.MI 012.MI.SA 014 017 018 023 025 027 029 031 032.MI 032.MI.SA
2.4 23 002 008 011 013 016 021 023 025 027.MI 027.MI.SA 029 031 033 034.MI 034.MI.SA 035 037 041 042 045 047 050 051
2.5 15 001 003 005 007 009.MI 009.MI.SA 011.MI 011.MI.SA 015 016 019 021 026 030 036
Chapter 3: Matrices
3.1 21 001 002 007 009 010 011 013 015 017 019 023 025 027 029 031 033 039 040 047 051 501.XP
3.2 31 005 007 009 011 013.MI 013.MI.SA 015.MI 015.MI.SA 017 019.MI 019.MI.SA 022 025.MI 025.MI.SA 027 031 033 039 041 043 045 046.MI 046.MI.SA 048 049.MI 049.MI.SA 050.MI 050.MI.SA 051.MI 051.MI.SA 055
3.3 33 003 005 007.MI 007.MI.SA 009 011 013 015 017 018 023.MI 023.MI.SA 025 027 028 029 031 033 037 039 041 042 045 047 049 051.MI 051.MI.SA 054 055 057 059 061 062
3.4 30 003 005 007 010 011 013 015.MI 015.MI.SA 017 020 023 025 029.MI 029.MI.SA 034 035 037 039 041 043 047 051 052 053 055 056.MI 056.MI.SA 057 059 061
3.5 18 001 003.MI 003.MI.SA 006 011.MI 011.MI.SA 015 018 021 023 026.MI 026.MI.SA 029 033 035 038 040 042
Chapter 4: Inequalities and Linear Programming
4.1 23 001.MI 001.MI.SA 003 005 006 007 011 013.MI 013.MI.SA 015 017 018 019 021 024 027 029.MI 029.MI.SA 031 032 034 035 036
4.2 24 001.MI 001.MI.SA 002 005 007 009 013.MI 013.MI.SA 015 017 020 022 023 025 027.MI 027.MI.SA 029 031 033 038 039 041 043 044
4.3 30 003.MI 003.MI.SA 005 007 009 011 013 015 017 019.MI 019.MI.SA 021 024 025 026 027 028 030 035 039.MI 039.MI.SA 042 043 045 046 048 050 052.MI 052.MI.SA 053
4.4 18 001.MI 001.MI.SA 004 005 007.MI 007.MI.SA 011 013 015 017 021 023.MI 023.MI.SA 025 028 029 032 034
4.5 25 001 003 005.MI 005.MI.SA 007 009 010 011.MI 011.MI.SA 013 015 018 019 020 021 023 025 027.MI 027.MI.SA 029 030 031 032 035 037
Chapter 5: Exponential and Logarithmic Functions
5.1 18 009.MI 009.MI.SA 011 013 015 017 018 025 026 033.MI 033.MI.SA 035 036 039 046 047 501.XP 502.XP
5.2 34 001 003 005.MI 005.MI.SA 007 009 011 013 015 017 019 021 023 025 027 029 033 035.MI 035.MI.SA 037 039 041 043 051.MI 051.MI.SA 052 053 055 063 064 067.MI 067.MI.SA 068 071
5.3 28 001.MI 001.MI.SA 003 005 007 009 011 013 015 017 019 021.MI 021.MI.SA 025 027.MI 027.MI.SA 029 031 035 037 040 043 045 047 051 055 058.MI 058.MI.SA
Chapter 6: Mathematics of Finance
6.1 27 003 009.MI 009.MI.SA 013 016.MI 016.MI.SA 019 021 023 025 027 028 031 033 035 037 038.MI 038.MI.SA 039 041 043 044 046.MI 046.MI.SA 048 049 052
6.2 39 003 005 007 008 009 010.MI 010.MI.SA 011 013 014.MI 014.MI.SA 021 023 025 028 031 032 033 034 037.MI 037.MI.SA 038 041 043 044 045 049 051 053 055 057 059 061 063 065.MI 065.MI.SA 067 069 071
6.3 25 005 009 010 011 012 013 014 015.MI 015.MI.SA 019 020 023 024 025 027.MI 027.MI.SA 030 033 035 039 041 042 043.MI 043.MI.SA 044
6.4 29 003.MI 003.MI.SA 005 007 008 009 011 015 017 019 020 021.MI 021.MI.SA 023 025 028 029 030 033 035 037 040 041 043 046 047 049.MI 049.MI.SA 051
6.5 19 001 003 005.MI 005.MI.SA 007 009 011 013 015.MI 015.MI.SA 017 020 021 023 025 032 036.MI 036.MI.SA 038
Chapter 7: Introduction to Probability
7.1 37 001 003 005 006 007 008 009 011.MI 011.MI.SA 015 017 019 021 023 025 027.MI 027.MI.SA 029 030 033 036 038 039 040 044.MI 044.MI.SA 045 046 048 050 052 053 055 057 060 062 064
7.2 24 005 007 010 016 017 019 021 023 025.MI 025.MI.SA 029 031 035 037 038.MI 038.MI.SA 039 040 042 044 047 048.MI 048.MI.SA 501.XP
7.3 35 001 003 005 007 010.MI 010.MI.SA 011 014 015 017 019 021 023 025 027 029 031.MI 031.MI.SA 033 035 037 039 041 043 044 045 047.MI 047.MI.SA 050 051 053 055 058 061.MI 061.MI.SA
7.4 17 003 005 007 013.MI 013.MI.SA 015 017 018 020 021 022.MI 022.MI.SA 023 024 029 501.XP 502.XP
7.5 29 001 003 005 007 009 011 012.MI 012.MI.SA 015 017 019 021 023 028.MI 028.MI.SA 030 031 033 034 036 037 039 040 042 044.MI 044.MI.SA 045 047 501.XP
7.6 26 001 003 004.MI 004.MI.SA 005 007 008 009 011 012.MI 012.MI.SA 013 015 017 019 020 021 022.MI 022.MI.SA 023 025 027 030 032 034 035
7.7 25 001 005 009 011 013 015 017 019 020.MI 020.MI.SA 021 023 024.MI 024.MI.SA 025 026 027 029 033.MI 033.MI.SA 034 036 037 038 039
Chapter 8: Further Topics in Probability; Data Description
8.1 16 001 009 011.MI 011.MI.SA 013 015 017.MI 017.MI.SA 021 023.MI 023.MI.SA 025 027 029 031.MI 031.MI.SA
8.2 30 001 005 007 009 011 013 015 017.MI 017.MI.SA 019 021 022 023 025 027 029 031 033.MI 033.MI.SA 035 038 040 042 044.MI 044.MI.SA 048 050 051 501.XP 502.XP
8.3 27 001 003 005 009 011 013 015 017 019.MI 019.MI.SA 021 023 026 028 029 033 035 037.MI 037.MI.SA 039 041 047 048.MI 048.MI.SA 051 053.MI 053.MI.SA
8.4 29 001 003 005 006 007 009 011 013 014 015.MI 015.MI.SA 017 019 021 023 025 028 030 031.MI 031.MI.SA 032 033 034 036 037 038.MI 038.MI.SA 039 041
8.5 21 001 005 007.MI 007.MI.SA 009 011 013 015 017 019 020 023 025.MI 025.MI.SA 027 029 032 034.MI 034.MI.SA 036 038
Chapter 9: Derivatives
9.1 37 002 004 006 008 010 011 013 016.MI 016.MI.SA 018 020 021.MI 021.MI.SA 022 024 027 029 031 033 035 037 040 042 044 046 048 051 053 055.MI 055.MI.SA 057 058.MI 058.MI.SA 061 063 065 067
9.2 28 001 003 005 007 008 009 011.MI 011.MI.SA 013 015 018 020 021 023 025 029 031 034 036 039 040.MI 040.MI.SA 043 045 047.MI 047.MI.SA 049 501.XP
9.3 27 001 003 007.MI 007.MI.SA 009 011 013 015 017 023 025 027.MI 027.MI.SA 029 030 031 033 035 037 039 040.MI 040.MI.SA 041 042.MI 042.MI.SA 047 048
9.4 33 001 003 004 005 007 009 011 014.MI 014.MI.SA 015 017 019 021 023 025 026.MI 026.MI.SA 027 030.MI 030.MI.SA 031 033 035 043 047 050 051 053 055 056 058.MI 058.MI.SA 061
9.5 31 002.MI 002.MI.SA 003 005 008 009 011 013 015 017.MI 017.MI.SA 020 021 022 023 025 030 031 034 036 038 039 041.MI 041.MI.SA 043 045.MI 045.MI.SA 046 049 051 054
9.6 37 003.MI 003.MI.SA 005 007 009 011.MI 011.MI.SA 013 015 016 018 020.MI 020.MI.SA 021.MI 021.MI.SA 023 025.MI 025.MI.SA 027 028 031.MI 031.MI.SA 033.MI 033.MI.SA 035.MI 035.MI.SA 037 038 039 042 044 045 047 048.MI 048.MI.SA 049 501.XP
9.7 27 001 003.MI 003.MI.SA 005 007 010 011 013 015 017 018 021.MI 021.MI.SA 023 025 027 029 031 033 035 037.MI 037.MI.SA 039 040.MI 040.MI.SA 041 043
9.8 25 001 003 005.MI 005.MI.SA 007 009 011 013 015.MI 015.MI.SA 017 019 021 024.MI 024.MI.SA 025 030 031 033 035.MI 035.MI.SA 036 037 038 041
9.9 20 001 006 009.MI 009.MI.SA 011 015 017 020.MI 020.MI.SA 023 025 027 029 031 034 035 036.MI 036.MI.SA 037 038
Chapter 10: Applications of Derivatives
10.1 32 001 003 005 007 009 015 017 019 021 025.MI 025.MI.SA 027 029 031 033 035 036 038 040 043 045 049.MI 049.MI.SA 051 052 053 054 055 057 058 060.MI 060.MI.SA
10.2 26 001 005 007 009 011 013 015 016 017 020.MI 020.MI.SA 021 023 026 028 029 031 034 035 037 038.MI 038.MI.SA 039 040.MI 040.MI.SA 501.XP
10.3 26 001 003 007.MI 007.MI.SA 009 012 013 014 017 019.MI 019.MI.SA 021 022 027 029 031 032 033.MI 033.MI.SA 035 037 039 040 042 043 045
10.4 18 001 003.MI 003.MI.SA 005 007 008 009 011 013.MI 013.MI.SA 015 019 022 023 029 031.MI 031.MI.SA 032
10.5 24 001 004 005.MI 005.MI.SA 007 009 011 013 015 017 019.MI 019.MI.SA 021 023 024 030 032 035 037 040.MI 040.MI.SA 041 042 043
Chapter 11: Derivatives Continued
11.1 32 001 003 005 007 009 011 013 015 017 019.MI 019.MI.SA 021 023 025 027 029 031 033 034 037 039 040 042 043 045 046 047 049.MI 049.MI.SA 050 051 052
11.2 32 001 003 005 007.MI 007.MI.SA 009 011 012 015 018 019 021 023 025 027.MI 027.MI.SA 029 030 033 038 039 043 044.MI 044.MI.SA 047 049 051 056 058 059 060 062
11.3 35 001 003 006 007.MI 007.MI.SA 009 011 013 015 017 019 020 022 023 025 027.MI 027.MI.SA 031 033 035 037 039 041 043 045 048 052 054 055 057 058.MI 058.MI.SA 059 061 062
11.4 22 001 003 005 007 009.MI 009.MI.SA 011 013 015 016 017 021 022 023 025 027 028.MI 028.MI.SA 030 033 035 037
11.5 14 001 003 006.MI 006.MI.SA 007 008 011 015 017 019.MI 019.MI.SA 021 024.MI 024.MI.SA
Chapter 12: Indefinite Integrals
12.1 32 001 003 005 007 009 011 013 015 017 019 021 024 025 027 029.MI 029.MI.SA 031 033 035 037 039 041.MI 041.MI.SA 043 045 047 048.MI 048.MI.SA 049 054 055 056
12.2 27 001 007 009.MI 009.MI.SA 013 015 017 019 021 023 025 027 029 031.MI 031.MI.SA 033 035 037 040 042 043 047.MI 047.MI.SA 051 053 055 056
12.3 28 001 004 005 007 009.MI 009.MI.SA 011 013 015 017 019 020 021 023 026.MI 026.MI.SA 027 029 032 035 037 041 043.MI 043.MI.SA 047 049 050 051
12.4 19 001 003.MI 003.MI.SA 004 007 009 011 012 014 015 019.MI 019.MI.SA 021 023 024 026 027.MI 027.MI.SA 501.XP
12.5 31 001 003 005 007 009 011.MI 011.MI.SA 013 015 017 019 022 024.MI 024.MI.SA 025 028 030 031 033 034 035 038 041 043 045 047 049 051 056.MI 056.MI.SA 061
Chapter 13: Definite Integrals: Techniques of Integration
13.1 22 001.MI 001.MI.SA 003 005 007 009 011 013 015 016.MI 016.MI.SA 018 020 022 024.MI 024.MI.SA 026 029 033 034 037 038
13.2 34 001 003 005 009 011 012 013 015 019 022 025 027 029 031.MI 031.MI.SA 037 038 039 041 043 044.MI 044.MI.SA 045 050 051 053 055 057 059 060 063 065 067.MI 067.MI.SA
13.3 26 001 003 005 007 009 011 013.MI 013.MI.SA 016 017 019 021 024 027.MI 027.MI.SA 029 030 032 033 038 039 040 041 043.MI 043.MI.SA 046
13.4 23 001 003 004 005 006 007 009 011 013.MI 013.MI.SA 015 017 019 021 023 025.MI 025.MI.SA 027 029 031 033 035.MI 035.MI.SA
13.5 30 001 003 005 007 008 009 011 013 014 015 017 018.MI 018.MI.SA 020 022 023 025 027 028.MI 028.MI.SA 029 031 033 036 037 038 039 040 041.MI 041.MI.SA
13.6 22 001 003 005.MI 005.MI.SA 007 009 011 013 015 016 017.MI 017.MI.SA 019 021 022 025 029 032.MI 032.MI.SA 033 035 036
13.7 28 001 003 005 006 008 010 011 013 015 017 018 019 020.MI 020.MI.SA 021 022 023 026 029 033.MI 033.MI.SA 036 038 039 040.MI 040.MI.SA 043 044
13.8 20 001 003 005 007 010 011 013.MI 013.MI.SA 015 017 019 021 023 024.MI 024.MI.SA 025 026.MI 026.MI.SA 029 030
Chapter 14: Functions of Two or More Variables
14.1 22 002 003 005.MI 005.MI.SA 007 009 012 013 015.MI 015.MI.SA 017 019 021 023 026.MI 026.MI.SA 030 033 035 036 037 038
14.2 33 001.MI 001.MI.SA 003 004 005 008 009 011 012 013 017.MI 017.MI.SA 019 021 023 025 027 029 031 033 035 037 039.MI 039.MI.SA 041 043 045 048 049 050 051 053 054
14.3 15 001 006 007 009 011 013.MI 013.MI.SA 017 019 020.MI 020.MI.SA 023 025 027 029
14.4 18 001 005 007 009 011.MI 011.MI.SA 013 015 016 019.MI 019.MI.SA 021 023 024 025 027.MI 027.MI.SA 029
14.5 18 001 003 004.MI 004.MI.SA 005 007 008 010 011 012 014.MI 014.MI.SA 015 017 021 023.MI 023.MI.SA 025
Total 2251