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Chapter E Answers to 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

Section 1.5 Limits at Infinity

Subsection 1.5.2 Exercises

Section 1.6 Continuity

Subsection 1.6.4 Exercises

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

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

Section 2.6 Using the Arithmetic of Derivatives – Examples

Subsection 2.6.2 Exercises

Section 2.7 Derivatives of Exponential Functions

Subsection 2.7.3 Exercises

Section 2.8 Derivatives of Trigonometric Functions

Subsection 2.8.8 Exercises

Section 2.9 One More Tool – the Chain Rule

Subsection 2.9.4 Exercises

Section 2.10 The Natural Logarithm

Subsection 2.10.3 Exercises

Section 2.11 Implicit Differentiation

Subsection 2.11.2 Exercises

Section 2.12 Inverse Trigonometric Functions

Subsection 2.12.2 Exercises

Section 2.13 The Mean Value Theorem

Subsection 2.13.5 Exercises

Section 2.14 Higher Order Derivatives

Subsection 2.14.2 Exercises

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

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

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

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

Section 3.7 L'Hôpital's Rule and Indeterminate Forms

Subsection 3.7.4 Exercises

Chapter 4 Towards Integral Calculus

Section 4.1 Introduction to Antiderivatives

Subsection 4.1.2 Exercises