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Appendix A Answers and Solutions to Selected Exercises

I Math 1560: Calculus I
1 Limits
1.1 An Introduction To Limits
1.1.3 Exercises

Problems

1.2 Epsilon-Delta Definition of a Limit

Exercises

1.3 Finding Limits Analytically

Exercises

Problems

1.4 One-Sided Limits

Exercises

Problems

1.5 Continuity

Exercises

Problems

1.6 Limits Involving Infinity
1.6.4 Exercises

Problems

2 Derivatives
2.1 Instantaneous Rates of Change: The Derivative
2.1.3 Exercises

Problems

2.2 Interpretations of the Derivative
2.2.5 Exercises

2.3 Basic Differentiation Rules
2.3.3 Exercises

Problems

2.4 The Product and Quotient Rules

Exercises

Problems

2.5 The Chain Rule

Exercises

Problems

2.6 Implicit Differentiation
2.6.4 Exercises

Problems

2.7 Derivatives of Inverse Functions

Exercises

3 The Graphical Behavior of Functions
3.1 Extreme Values

Exercises

Problems

3.2 The Mean Value Theorem

Exercises

3.3 Increasing and Decreasing Functions

Exercises

Problems

3.4 Concavity and the Second Derivative
3.4.3 Exercises

Problems

3.5 Curve Sketching

Exercises

4 Applications of the Derivative
4.1 Newton's Method

Exercises

4.2 Related Rates

Exercises

4.3 Optimization

Exercises

4.4 Differentials

Exercises

Problems

4.5 Taylor Polynomials

Exercises

5 Integration
5.1 Antiderivatives and Indefinite Integration

Exercises

5.2 The Definite Integral

Exercises

Problems

5.3 Riemann Sums
5.3.4 Exercises

Problems

5.4 The Fundamental Theorem of Calculus
5.4.6 Exercises

Problems

5.5 Numerical Integration
5.5.6 Exercises

Problems

II Math 2560: Calculus II
6 Techniques of Antidifferentiation
6.1 Substitution
6.1.5 Exercises

Problems

6.2 Integration by Parts

Exercises

Problems

6.3 Trigonometric Integrals
6.3.4 Exercises

Problems

6.4 Trigonometric Substitution

Exercises

6.5 Partial Fraction Decomposition

Exercises

6.6 Hyperbolic Functions
6.6.3 Exercises

Problems

6.7 L'Hospital's Rule
6.7.4 Exercises

Problems

6.8 Improper Integration
6.8.4 Exercises

Problems

7 Applications of Integration
7.1 Area Between Curves

Exercises

7.2 Volume by Cross-Sectional Area; Disk and Washer Methods

Exercises

7.3 The Shell Method

Exercises

7.4 Arc Length and Surface Area
7.4.3 Exercises

Problems

7.5 Work
7.5.4 Exercises

7.6 Fluid Forces

Exercises

8 Differential Equations
8.1 Graphical and Numerical Solutions to Differential Equations
8.1.4 Exercises

8.2 Separable Differential Equations
8.2.2 Exercises

8.3 First Order Linear Differential Equations
8.3.2 Exercises

8.4 Modeling with Differential Equations
8.4.3 Exercises

9 Curves in the Plane
9.1 Conic Sections
9.1.4 Exercises

Problems

9.2 Parametric Equations
9.2.4 Exercises

Problems

9.3 Calculus and Parametric Equations
9.3.4 Exercises

Problems

9.4 Introduction to Polar Coordinates
9.4.4 Exercises

Problems

9.5 Calculus and Polar Functions
9.5.5 Exercises

Problems

III Math 2570: Calculus III
10 Sequences and Series
10.1 Sequences

Exercises

Problems

10.2 Infinite Series
10.2.4 Exercises

Problems

10.3 Integral and Comparison Tests
10.3.4 Exercises

Problems

10.4 Ratio and Root Tests
10.4.3 Exercises

Problems

10.5 Alternating Series and Absolute Convergence

Exercises

10.6 Power Series

Exercises

Problems

10.7 Taylor Series

Exercises

Problems

11 Vectors
11.1 Introduction to Cartesian Coordinates in Space
11.1.7 Exercises

Problems

11.2 An Introduction to Vectors

Exercises

Problems

11.3 The Dot Product
11.3.2 Exercises

Problems

11.4 The Cross Product
11.4.3 Exercises

Problems

11.5 Lines
11.5.4 Exercises

Problems

11.6 Planes
11.6.2 Exercises

Problems

12 Vector Valued Functions
12.1 Vector-Valued Functions
12.1.4 Exercises

Problems

12.2 Calculus and Vector-Valued Functions
12.2.5 Exercises

Problems

12.3 The Calculus of Motion
12.3.3 Exercises