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Business Economics

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INTRODUCTION TO CALCULUS FOR BUSINESS AND ECONOMICS

RAMA SHANKER, Ph.D.

Associate Professor of Statistics

Department of Statistics Eritrea Institute of Technology MAINEFHI, ASMARA, ERITREA


RAVI SHANKER, Ph.D.

Assistant Professor of Mathematics & Head Department of Mathematics

G.L.A. College

Nilambar Pitambar University

Medininagar, Daltanganj, Jharkhand, India

CONTENTS

Chapter I : Functions Page 1-53
1.1. Introduction 1
1.2. Functions 1
1.3. Intervals 6
1.4. Types of Functions 6
1.4.1. Constant Function 6
1.4.2. Identity Function 7
1.4.3. Absolute Value Function 7
1.4.4. Linear Functions 7
1.4.5. Quadratic Functions 8
1.4.6. Polynomial Functions 9
1.4.7. Rational Functions 10
1.4.8. One-to-one Function 11
1.4.9. Odd and Even Functions 11
1.4.10. Monotonic Functions 13
1.4.11. Composite Functions 13
1.4.12. Inverse Functions 15
1.4.13. Explicit and Implicit Functions 17
1.4.14. Exponential Functions 17
1.4.15. Logarithmic Functions 21
1.4.16. Power Functions 23
1.4.17. Homogeneous Functions 25
1.4.18. Homothetic Functions 28
1.4.19. Concave and Convex Functions 31
1.4.20. Periodic Functions 32
1.5. Functions in Business and Economics 32
1.5.1. Demand Function 32
1.5.2. Supply Function 33
1.5.3. Cost Function 35
1.5.4. Revenue Function 35
1.5.5. Profit Function 35
1.5.6. Consumption Function 36
1.6. The algebra of Functions 36
1.7. Vertical and Horizontal Translation of Functions 37
1.8. Applications of Linear Functions in Business and Economics 39
1.9. Applications of Non-linear Functions in Business and Economics 45
Chapter II : Limits and Continuity of Functions 54-108
2.1. Introduction 54
2.2. The Concept of Limit 54
2.3. Properties of Limits and Evaluation of Limits 56
2.4. One Sided Limits 69
2.5. Limits at Infinity and Infinite Limit 73
2.6. The Concept of Continuity 78
2.7. One-Sided Continuity 84
.8. Continuity on Intervals 85
2.9. Types of Discontinuity 90
2.10. The Intermediate Value Theorem (IVT) 93
2.11. Asymptotes of Function 95
2.12. Applications of Limit and Continuity to Business and Economics. 100
Chapter III : Differentiation 109-186
3.1. Introduction 109
3.2. The Slope of a Graph 109
3.3. The Derivative of a Function 116
3.4. Differentiability and Continuity 120
3.5. Differentiability and Linear Approximations 122
3.6. Rules of Differentiation 125
3.7. The Chain Rule and Composite Functions 135
3.8. Derivatives of Logarithmic and Exponential Functions 143
3.9. Implicit Differentiation 152
3.10. Derivative of Inverse of a Function 159
3.11. Derivative of a Function in Parametric Form 161
3.12. Derivative of a Function with respect to another Function 165
3.13. Logarithmic Differentiation 166
3.14. Successive Differentiation 173
3.15. nth Derivative of some Standard Functions 179
3.16. Leibnitz's Theorem. 182
3.17. Second Derivative in Parametric Form. 185
Chapter IV : Further Topics in Differentiation 187-122
4.1. Introduction 187
4.2. Increasing and Decreasing Functions 187
4.3. Relative Maxima and Minima of a Function 193
4.4. Global Maxima and Minima of a Function 204
4.5. Concavity and Convexity of a Function 209
4.6. Rolle's and Lagrange's Mean Value Theorem 219
Chapter V : Applications of Differentiation to Business and Economics 223-316
5.1. Introduction 223
5.2. Average and Marginal Functions 223
.3. Marginal Revenue Product 232
5.4. Marginal Propensity to Consume and Save 233
5.5. The Investment Multiplier 236
5.6. The Money Multiplier 238
5.7. The Elasticity of Functions 239
5.8. Rate of Change, Relative Rate of Change and Related Rates 257
.9. Univariate Utility Function and Risk Aversion 264
5.10. Monopoly Problems 271
5.11. Effect of Taxation under Pure Competition 281
5.12. Effects of Taxation and Subsidy on Monopoly 284
5.13. Law of diminishing Returns 297
5.14. Applied Optimization Problems 300
Chapter VI : Partial Differentiation 317-358
6.1. Introduction 317
.2. Functions of Several Independent Variables 317
.3. Partial Differentiation 318
6.4. Rules of Partial Differentiation 319
6.5. Composite Functions and the Chain Rule 324
6.6. Second Order Partial Derivatives and Young's Theorem 327
6.7. Homogeneous Functions and Euler's Theorem 330
6.8.
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When she reached the first hills of the Italic Mountains, she had a last view back on the skyline of her hometown Bookmarksgrov


Jacob Webb 14 March 2019

When she reached the first hills of the Italic Mountains, she had a last view back on the skyline of her hometown Bookmarksgrov

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