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Appendix A Answers to Selected Exercises
Below you will find answers to selected exercises from the end of each section. Worked solutions are not provided, so you are encouraged to discuss your thought process and reasoning for exercises with others, even if your final answer matches what is listed here. Your process and reasoning are the most important things for deepening your understanding and ensuring you can use important concepts on your own in the future, so use this section as a guide, but not a replacement for engaging in the exercises with others.
1 Functions As Models 1.1 Biology and Calculus 1.1.4 Exercises
1.1.4.1.
1.2 Functions 1.2.8 Exercises
1.2.8.3. 1.2.8.5. 1.2.8.6.
1.3 Units and Dimensions of Functions 1.3.5 Exercises
1.3.5.2.
1.4 Linear Functions 1.4.5 Exercises
1.4.5.2. 1.4.5.3. 1.4.5.4.
1.5 Exponential and Logarithmic Functions 1.5.5 Exercises
1.5.5.1. 1.5.5.2. 1.5.5.3. 1.5.5.4.
1.6 Trigonometric Functions 1.6.4 Exercises
1.6.4.1. 1.6.4.2. 1.6.4.3. 1.6.4.4.
1.7 Discrete-Time Dynamical Systems 1.7.4 Exercises
1.7.4.2. 1.7.4.3.
1.8 Analyzing Discrete-Time Dynamical Systems 1.8.4 Exercises
1.8.4.1.
1.9 Applications: The Lung Model and Competing Species 1.9.4 Exercises
1.9.4.1. 1.9.4.2. 1.9.4.4. 1.9.4.5.
2 The Derivative 2.1 Limits of Functions 2.1.4 Exercises
2.1.4.1. 2.1.4.2. 2.1.4.4.
2.2 The Derivative of a Function at a Point 2.2.3 Exercises
2.2.3.1. 2.2.3.3. 2.2.3.4.
2.3 The Derivative Function 2.3.3 Exercises
2.3.3.2. 2.3.3.3.
2.4 The Second Derivative 2.4.5 Exercises
2.4.5.1. 2.4.5.2.
2.5 Elementary Derivative Rules 2.5.5 Exercises
2.5.5.1. 2.5.5.2.
2.6 Derivatives of the Sine and Cosine Functions 2.6.3 Exercises
2.6.3.1. 2.6.3.2. 2.6.3.3.
2.7 Derivatives of Products and Quotients 2.7.5 Exercises
2.7.5.2. 2.7.5.3. 2.7.5.4. 2.7.5.5.
2.8 Derivatives of Compositions 2.8.5 Exercises
2.8.5.1. 2.8.5.2. 2.8.5.3. 2.8.5.4.
2.9 Derivatives of Inverse Functions 2.9.5 Exercises
2.9.5.1. 2.9.5.2. 2.9.5.3. 2.9.5.4.
3 Using the Derivative 3.1 Linear and Quadratic Approximation 3.1.5 Exercises
3.1.5.1. 3.1.5.2. 3.1.5.3.
3.2 The Stability Theorem 3.2.4 Exercises
3.2.4.3.
3.3 The Logistic Discrete-Time Dynamical System 3.3.4 Exercises
3.3.4.1.
3.4 Identifying Extreme Values of Functions 3.4.4 Exercises
3.4.4.1. 3.4.4.2. 3.4.4.3.
3.5 Global Optimization and Applications 3.5.4 Exercises
3.5.4.1. 3.5.4.2. 3.5.4.3.
3.6 Limits: L’Hôpital’s Rule 3.6.4 Exercises
3.6.4.1. 3.6.4.2. 3.6.4.3.
3.7 Limits: Leading Behaviors 3.7.4 Exercises
3.7.4.1.
4 Continuous-Time Dynamical Systems 4.1 Introduction to Differential Equations and Antiderivatives 4.1.4 Exercises
4.1.4.1. 4.1.4.2.
4.2 Solving Pure-Time Differential Equations 4.2.4 Exercises
4.2.4.1. 4.2.4.2. 4.2.4.3. 4.2.4.4.
4.3 Riemann Sums 4.3.6 Exercises
4.3.6.1. 4.3.6.2. 4.3.6.3. 4.3.6.4.
4.4 The Definite Integral 4.4.5 Exercises
4.4.5.1. 4.4.5.2. 4.4.5.3. 4.4.5.4.
4.5 The Fundamental Theorem of Calculus 4.5.5 Exercises
4.5.5.1. 4.5.5.2. 4.5.5.3.
4.6 Approximations of Solutions 4.6.4 Exercises
4.6.4.1. 4.6.4.2.
