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Calculus Early Transcendentals:
Differential & Multi-Variable Calculus for Social Sciences
Contents
Index
Calc
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Contents
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Front Matter
Copyright
Acknowledgements
Open Educational Resources (OER) Support: Corrections and Suggestions
Dedication
Introduction
Problem Solving Strategies
1
Review
Algebra
Analytic Geometry
Trigonometry
Additional Exercises
2
Functions
All About Functions
Symmetry, Transformations and Compositions
Exponential Functions
Inverse Functions
Logarithmic Functions
Trigonometric Functions
Economic Models
Additional Exercises
3
Limits and Continuity
The Limit
Precise Definition of a Limit
Computing Limits: Graphically
Computing Limits: Algebraically
Limits at Infinity, Infinite Limits and Asymptotes
The Squeeze Theorem
Continuity and IVT
4
Derivatives
The Rate of Change of a Function
The Derivative Function
Derivative Rules
The Chain Rule
Derivative Rules for Trigonometric Functions
Derivatives of Exponential & Logarithmic Functions
Implicit and Logarithmic Differentiation
Derivatives of Inverse Functions
Additional Exercises
5
Applications of Derivatives
Elasticity of Demand
Related Rates
Linear and Higher Order Approximations
Indeterminate Form & L'Hôpital's Rule
Extrema of a Function
The Mean Value Theorem
Curve Sketching
Optimization Problems
6
Three Dimensions
The Coordinate System
Vectors
The Dot Product
The Cross Product
Lines and Planes
Other Coordinate Systems
7
Multi-Variable Calculus
Functions of Several Variables
Limits and Continuity
Partial Differentiation
The Chain Rule
Directional Derivatives
Maxima and Minima
Lagrange Multipliers
Back Matter
Index
Authored in PreTeXt
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Chapter
3
Limits and Continuity
¶
3.1
The Limit
3.2
Precise Definition of a Limit
3.3
Computing Limits: Graphically
3.4
Computing Limits: Algebraically
3.5
Limits at Infinity, Infinite Limits and Asymptotes
3.6
The Squeeze Theorem
3.7
Continuity and IVT
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