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Solutions A Answers and Solutions to Selected Exercises

Part I Math 1560: Calculus I

Chapter 1 Limits

Section 1.1 An Introduction To Limits
Exercises 1.1.3 Exercises
Section 1.2 Epsilon-Delta Definition of a Limit
Exercises Exercises
Section 1.3 Finding Limits Analytically
Exercises Exercises
Terms and Concepts
Problems
Section 1.4 One-Sided Limits
Exercises Exercises
Problems
Section 1.5 Continuity
Exercises Exercises
Section 1.6 Limits Involving Infinity
Exercises 1.6.4 Exercises
Problems

Chapter 2 Derivatives

Section 2.1 Instantaneous Rates of Change: The Derivative
Exercises 2.1.3 Exercises
Problems
Section 2.2 Interpretations of the Derivative
Exercises 2.2.5 Exercises
Section 2.3 Basic Differentiation Rules
Exercises 2.3.3 Exercises
Problems
Section 2.4 The Product and Quotient Rules
Exercises Exercises
Problems
Section 2.5 The Chain Rule
Exercises Exercises
Problems
Section 2.6 Implicit Differentiation
Exercises 2.6.4 Exercises
Problems
Section 2.7 Derivatives of Inverse Functions
Exercises Exercises
Terms and Concepts

Chapter 3 The Graphical Behavior of Functions

Section 3.1 Extreme Values
Exercises Exercises
Problems
Section 3.2 The Mean Value Theorem
Exercises Exercises
Section 3.3 Increasing and Decreasing Functions
Exercises Exercises
Problems
Section 3.4 Concavity and the Second Derivative
Exercises 3.4.3 Exercises
Problems
Section 3.5 Curve Sketching
Exercises Exercises

Chapter 4 Applications of the Derivative

Section 4.1 Newton's Method
Exercises Exercises
Section 4.2 Related Rates
Exercises Exercises
Section 4.3 Optimization
Exercises Exercises
Section 4.4 Differentials
Exercises Exercises
Section 4.5 Taylor Polynomials
Exercises Exercises

Chapter 5 Integration

Section 5.1 Antiderivatives and Indefinite Integration
Exercises Exercises
Section 5.2 The Definite Integral
Exercises Exercises
Problems
Section 5.3 Riemann Sums
Exercises 5.3.4 Exercises
Problems
Section 5.4 The Fundamental Theorem of Calculus
Exercises 5.4.6 Exercises
Problems
Section 5.5 Numerical Integration
Exercises 5.5.6 Exercises
Problems

Part II Math 2560: Calculus II

Chapter 6 Techniques of Antidifferentiation

Section 6.1 Substitution
Exercises 6.1.5 Exercises
Problems
Section 6.2 Integration by Parts
Exercises Exercises
Problems
Section 6.3 Trigonometric Integrals
Exercises 6.3.4 Exercises
Section 6.4 Trigonometric Substitution
Exercises Exercises
Section 6.5 Partial Fraction Decomposition
Exercises Exercises
Section 6.6 Hyperbolic Functions
Exercises 6.6.3 Exercises
Problems
Section 6.7 L'Hospital's Rule
Exercises 6.7.4 Exercises
Problems
Section 6.8 Improper Integration
Exercises 6.8.4 Exercises
Problems

Chapter 7 Applications of Integration

Section 7.1 Area Between Curves
Exercises Exercises
Section 7.2 Volume by Cross-Sectional Area; Disk and Washer Methods
Exercises Exercises
Section 7.3 The Shell Method
Exercises Exercises
Section 7.5 Work
Exercises 7.5.4 Exercises
Section 7.6 Fluid Forces
Exercises Exercises

Chapter 8 Differential Equations

Section 8.1 Graphical and Numerical Solutions to Differential Equations
Exercises 8.1.4 Exercises
Section 8.2 Separable Differential Equations
Exercises 8.2.2 Exercises
Section 8.3 First Order Linear Differential Equations
Exercises 8.3.2 Exercises
Section 8.4 Modeling with Differential Equations
Exercises 8.4.3 Exercises

Chapter 9 Curves in the Plane

Section 9.1 Conic Sections
Exercises 9.1.4 Exercises
Problems
Section 9.2 Parametric Equations
Exercises 9.2.4 Exercises
Problems
Section 9.3 Calculus and Parametric Equations
Exercises 9.3.4 Exercises
Problems
Section 9.4 Introduction to Polar Coordinates
Exercises 9.4.4 Exercises
Problems
Section 9.5 Calculus and Polar Functions
Exercises 9.5.5 Exercises
Problems

Part III Math 2570: Calculus III

Chapter 10 Sequences and Series

Section 10.1 Sequences
Exercises Exercises
Problems
Section 10.2 Infinite Series
Exercises 10.2.4 Exercises
Problems
Section 10.3 Integral and Comparison Tests
Exercises 10.3.4 Exercises
Problems
Section 10.4 Ratio and Root Tests
Exercises 10.4.3 Exercises
Problems
Section 10.5 Alternating Series and Absolute Convergence
Exercises Exercises
Section 10.6 Power Series
Exercises Exercises
Problems
Section 10.7 Taylor Series
Exercises Exercises
Problems

Chapter 11 Vectors

Section 11.1 Introduction to Cartesian Coordinates in Space
Exercises 11.1.7 Exercises
Section 11.2 An Introduction to Vectors
Exercises Exercises
Problems
Section 11.3 The Dot Product
Exercises 11.3.2 Exercises
Problems
Section 11.4 The Cross Product
Exercises 11.4.3 Exercises
Problems
Section 11.5 Lines
Exercises 11.5.2 Exercises
Problems
Section 11.6 Planes
Exercises 11.6.2 Exercises
Problems

Chapter 12 Vector Valued Functions

Section 12.1 Vector-Valued Functions
Exercises 12.1.4 Exercises
Problems
Section 12.2 Calculus and Vector-Valued Functions
Exercises 12.2.5 Exercises
Problems
Section 12.3 The Calculus of Motion
Exercises 12.3.3 Exercises
Problems
Section 12.4 Unit Tangent and Normal Vectors
Exercises 12.4.4 Exercises
Problems
Section 12.5 The Arc Length Parameter and Curvature
Exercises 12.5.3 Exercises
Problems

Chapter 13 Introduction to Functions of Several Variables

Section 13.1 Introduction to Multivariable Functions
Exercises 13.1.5 Exercises
Section 13.2 Limits and Continuity of Multivariable Functions
Exercises 13.2.5 Exercises
Section 13.3 Partial Derivatives
Exercises 13.3.7 Exercises
Problems

Part IV Math 2580: Calculus IV

Chapter 14 Functions of Several Variables, Continued

Section 14.1 Differentiability and the Total Differential
Exercises 14.1.6 Exercises
Section 14.2 The Multivariable Chain Rule
Exercises 14.2.3 Exercises
Problems
Section 14.3 Directional Derivatives
Exercises 14.3.3 Exercises
Problems
Section 14.4 Tangent Lines, Normal Lines, and Tangent Planes
Exercises 14.4.5 Exercises
Section 14.5 Extreme Values
Exercises 14.5.3 Exercises

Chapter 15 Multiple Integration

Section 15.1 Iterated Integrals and Area
Exercises 15.1.4 Exercises
Section 15.2 Double Integration and Volume
Exercises Exercises
Section 15.3 Double Integration with Polar Coordinates
Exercises Exercises