Active Calculus

Appendix C Answers to Selected Exercises

1 Understanding the Derivative
1.1 How do we measure velocity?
1.1.4 Exercises

1.2 The notion of limit
1.2.4 Exercises

1.3 The derivative of a function at a point
1.3.3 Exercises

1.4 The derivative function
1.4.3 Exercises

1.5 Interpreting, estimating, and using the derivative
1.5.4 Exercises

1.6 The second derivative
1.6.5 Exercises

1.7 Limits, Continuity, and Differentiability
1.7.5 Exercises

1.8 The Tangent Line Approximation
1.8.4 Exercises

2 Computing Derivatives
2.1 Elementary derivative rules
2.1.5 Exercises

2.2 The sine and cosine functions
2.2.3 Exercises

2.3 The product and quotient rules
2.3.5 Exercises

2.4 Derivatives of other trigonometric functions
2.4.3 Exercises

2.5 The chain rule
2.5.5 Exercises

2.6 Derivatives of Inverse Functions
2.6.6 Exercises

2.7 Derivatives of Functions Given Implicitly
2.7.3 Exercises

2.8 Using Derivatives to Evaluate Limits
2.8.4 Exercises

3 Using Derivatives
3.1 Using derivatives to identify extreme values
3.1.4 Exercises

3.2 Using derivatives to describe families of functions
3.2.3 Exercises

3.3 Global Optimization
3.3.4 Exercises

3.4 Applied Optimization
3.4.3 Exercises

3.5 Related Rates
3.5.3 Exercises

4 The Definite Integral
4.1 Determining distance traveled from velocity
4.1.5 Exercises

4.2 Riemann Sums
4.2.5 Exercises

4.3 The Definite Integral
4.3.5 Exercises

4.4 The Fundamental Theorem of Calculus
4.4.5 Exercises

5 Evaluating Integrals
5.1 Constructing Accurate Graphs of Antiderivatives
5.1.5 Exercises

5.2 The Second Fundamental Theorem of Calculus
5.2.5 Exercises

5.3 Integration by Substitution
5.3.5 Exercises

5.4 Integration by Parts
5.4.7 Exercises

5.5 Other Options for Finding Algebraic Antiderivatives
5.5.5 Exercises

5.6 Numerical Integration
5.6.6 Exercises

6 Using Definite Integrals
6.1 Using Definite Integrals to Find Area and Length
6.1.5 Exercises

6.2 Using Definite Integrals to Find Volume
6.2.5 Exercises

6.3 Density, Mass, and Center of Mass
6.3.5 Exercises

6.4 Physics Applications: Work, Force, and Pressure
6.4.5 Exercises

6.5 Improper Integrals
6.5.5 Exercises

7 Differential Equations
7.1 An Introduction to Differential Equations
7.1.5 Exercises

7.2 Qualitative behavior of solutions to DEs
7.2.4 Exercises

7.3 Euler's method
7.3.4 Exercises

7.4 Separable differential equations
7.4.3 Exercises

7.5 Modeling with differential equations
7.5.3 Exercises

7.6 Population Growth and the Logistic Equation
7.6.4 Exercises

8 Sequences and Series
8.1 Sequences
8.1.3 Exercises

8.2 Geometric Series
8.2.3 Exercises

8.3 Series of Real Numbers
8.3.7 Exercises

8.4 Alternating Series
8.4.6 Exercises

8.5 Taylor Polynomials and Taylor Series
8.5.6 Exercises

8.6 Power Series
8.6.4 Exercises