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Chapter D Hints for Exercises

Chapter 1 Limits

Section 1.1 Drawing Tangents and a First Limit

Subsection 1.1.2 Exercises

Section 1.2 Another Limit and Computing Velocity

Subsection 1.2.2 Exercises

Section 1.3 The Limit of a Function

Subsection 1.3.2 Exercises

Section 1.4 Calculating Limits with Limit Laws

Subsection 1.4.2 Exercises

1.4.2.10 (✳)
1.4.2.14 (✳)
1.4.2.15 (✳)
1.4.2.16 (✳)
1.4.2.17 (✳)
1.4.2.18 (✳)
1.4.2.20 (✳)
1.4.2.21 (✳)
1.4.2.22 (✳)
1.4.2.23 (✳)
1.4.2.24 (✳)
1.4.2.27 (✳)
1.4.2.35 (✳)
1.4.2.36 (✳)
1.4.2.43 (✳)

Section 1.5 Limits at Infinity

Subsection 1.5.2 Exercises

1.5.2.10 (✳)
1.5.2.11 (✳)
1.5.2.12 (✳)
1.5.2.13 (✳)
1.5.2.14 (✳)
1.5.2.15 (✳)
1.5.2.17 (✳)
1.5.2.20 (✳)
1.5.2.22 (✳)
1.5.2.24 (✳)

Section 1.6 Continuity

Subsection 1.6.4 Exercises

1.6.4.13 (✳)
1.6.4.14 (✳)
1.6.4.15 (✳)
1.6.4.16 (✳)
1.6.4.17 (✳)
1.6.4.18 (✳)
1.6.4.19 (✳)
1.6.4.20 (✳)
1.6.4.22 (✳)
1.6.4.23 (✳)
1.6.4.24 (✳)
1.6.4.25 (✳)

Chapter 2 Derivatives

Section 2.1 Revisiting Tangent Lines

Subsection 2.1.2 Exercises

Section 2.2 Definition of the Derivative

Subsection 2.2.4 Exercises

2.2.4.11 (✳)
2.2.4.12 (✳)
2.2.4.15 (✳)
2.2.4.16 (✳)
2.2.4.17 (✳)
2.2.4.19 (✳)
2.2.4.20 (✳)
2.2.4.21 (✳)
2.2.4.22 (✳)
2.2.4.26 (✳)
2.2.4.27 (✳)

Section 2.3 Interpretations of the Derivative

Subsection 2.3.3 Exercises

Section 2.4 Arithmetic of Derivatives - a Differentiation Toolbox

Subsection 2.4.2 Exercises

2.4.2.14 (✳)

Section 2.6 Using the Arithmetic of Derivatives – Examples

Subsection 2.6.2 Exercises

2.6.2.13 (✳)
2.6.2.17 (✳)
2.6.2.19 (✳)

Section 2.7 Derivatives of Exponential Functions

Subsection 2.7.3 Exercises

2.7.3.14 (✳)

Section 2.8 Derivatives of Trigonometric Functions

Subsection 2.8.8 Exercises

2.8.8.14 (✳)
2.8.8.16 (✳)
2.8.8.17 (✳)
2.8.8.18 (✳)
2.8.8.20 (✳)
2.8.8.21 (✳)
2.8.8.28 (✳)
2.8.8.29 (✳)
2.8.8.30 (✳)

Section 2.9 One More Tool – the Chain Rule

Subsection 2.9.4 Exercises

2.9.4.10 (✳)
2.9.4.11 (✳)
2.9.4.12 (✳)
2.9.4.18 (✳)
2.9.4.19 (✳)
2.9.4.20 (✳)
2.9.4.21 (✳)
2.9.4.22 (✳)
2.9.4.23 (✳)
2.9.4.24 (✳)
2.9.4.27 (✳)
2.9.4.30 (✳)
2.9.4.32 (✳)

Section 2.10 The Natural Logarithm

Subsection 2.10.3 Exercises

2.10.3.11 (✳)
2.10.3.12 (✳)
2.10.3.13 (✳)
2.10.3.14 (✳)
2.10.3.15 (✳)
2.10.3.18 (✳)
2.10.3.20 (✳)
2.10.3.24 (✳)
2.10.3.25 (✳)
2.10.3.26 (✳)
2.10.3.27 (✳)
2.10.3.28 (✳)
2.10.3.29 (✳)

Section 2.11 Implicit Differentiation

Subsection 2.11.2 Exercises

2.11.2.4 (✳)
2.11.2.5 (✳)
2.11.2.6 (✳)
2.11.2.8 (✳)
2.11.2.10 (✳)
2.11.2.12 (✳)
2.11.2.13 (✳)
2.11.2.14 (✳)

Section 2.12 Inverse Trigonometric Functions

Subsection 2.12.2 Exercises

2.12.2.13 (✳)
2.12.2.18 (✳)
2.12.2.20 (✳)
2.12.2.21 (✳)
2.12.2.22 (✳)

Section 2.13 The Mean Value Theorem

Subsection 2.13.5 Exercises

2.13.5.7 (✳)
2.13.5.15 (✳)
2.13.5.16 (✳)
2.13.5.18 (✳)

Section 2.14 Higher Order Derivatives

Subsection 2.14.2 Exercises

2.14.2.17 (✳)
2.14.2.18 (✳)
2.14.2.22 (✳)

Chapter 3 Applications of derivatives

Section 3.1 Velocity and Acceleration

Subsection 3.1.2 Exercises

Section 3.2 Related Rates

Subsection 3.2.2 Exercises

3.2.2.13 (✳)
3.2.2.15 (✳)

Section 3.3 Exponential Growth and Decay — a First Look at Differential Equations

Subsection 3.3.4 Exercises

Subsubsection Exercises for § 3.3.1

Subsubsection Exercises for § 3.3.2

Subsubsection Exercises for § 3.3.3

Subsubsection Further problems for § 3.3

Section 3.4 Approximating Functions Near a Specified Point — Taylor Polynomials

Subsection 3.4.11 Exercises

Subsubsection Exercises for § 3.4.1

Subsubsection Exercises for § 3.4.2

Subsubsection Exercises for § 3.4.3

Subsubsection Exercises for § 3.4.4

Subsubsection Exercises for § 3.4.5

Subsubsection Exercises for § 3.4.6

Subsubsection Exercises for § 3.4.7

Subsubsection Exercises for § 3.4.8

Subsubsection Further problems for § 3.4

3.4.11.1 (✳)
3.4.11.3 (✳)
3.4.11.5 (✳)
3.4.11.6 (✳)
3.4.11.7 (✳)
3.4.11.8 (✳)
3.4.11.9 (✳)
3.4.11.10 (✳)
3.4.11.11 (✳)
3.4.11.12 (✳)
3.4.11.13 (✳)
3.4.11.14 (✳)
3.4.11.17 (✳)
3.4.11.19 (✳)
3.4.11.22 (✳)

Section 3.5 Optimisation

Subsection 3.5.4 Exercises

Subsubsection Exercises for § 3.5.1

Subsubsection Exercises for § 3.5.2

Subsubsection Exercises for § 3.5.3

3.5.4.10 (✳)
3.5.4.11 (✳)
3.5.4.12 (✳)
3.5.4.14 (✳)
3.5.4.15 (✳)

Section 3.6 Sketching Graphs

Subsection 3.6.7 Exercises

Subsubsection Exercises for § 3.6.1

Subsubsection Exercises for § 3.6.2

Subsubsection Exercises for § 3.6.3

Subsubsection Exercises for § 3.6.4

Subsubsection Exercises for § 3.6.6

3.6.7.11 (✳)
3.6.7.12 (✳)
3.6.7.14 (✳)

Section 3.7 L'Hôpital's Rule and Indeterminate Forms

Subsection 3.7.4 Exercises

3.7.4.10 (✳)
3.7.4.15 (✳)
3.7.4.17 (✳)
3.7.4.23 (✳)
3.7.4.24 (✳)

Chapter 4 Towards Integral Calculus

Section 4.1 Introduction to Antiderivatives

Subsection 4.1.2 Exercises

4.1.2.20 (✳)