Chapter 5 Logarithmic Exponential and Other Transcendental Functions

Chapter 5 Logarithmic, Exponential, and Other Transcendental Functions

Definition of the Natural Logarithmic Function and Figure 5. 1 Copyright © Houghton Mifflin Company. All rights reserved. 2

Theorem 5. 1 Properties of the Natural Logarithmic Function Copyright © Houghton Mifflin Company. All rights reserved. 3

Theorem 5. 2 Logarithmic Properties Copyright © Houghton Mifflin Company. All rights reserved. 4

Definition of e and Figure 5. 5 Copyright © Houghton Mifflin Company. All rights reserved. 5

Theorem 5. 3 Derivative of the Natural Logarithmic Function Copyright © Houghton Mifflin Company. All rights reserved. 6

Theorem 5. 4 Derivative Involving Absolute Value Copyright © Houghton Mifflin Company. All rights reserved. 7

Theorem 5. 5 Log Rule for Integration Copyright © Houghton Mifflin Company. All rights reserved. 8

Guidelines for Integration Copyright © Houghton Mifflin Company. All rights reserved. 9

Integrals of the Six Basic Trigonometric Functions Copyright © Houghton Mifflin Company. All rights reserved. 10

Definition of Inverse Function and Figure 5. 10 Copyright © Houghton Mifflin Company. All rights reserved. 11

Theorem 5. 6 Reflective Property of Inverse Functions and Figure 5. 12 Copyright © Houghton Mifflin Company. All rights reserved. 12

Theorem 5. 7 The Existence of an Inverse Function and Figure 5. 13 Copyright © Houghton Mifflin Company. All rights reserved. 13

Guidelines for Finding an Inverse Function Copyright © Houghton Mifflin Company. All rights reserved. 14

Theorem 5. 8 Continuity and Differentiability of Inverse Functions Copyright © Houghton Mifflin Company. All rights reserved. 15

Theorem 5. 9 The Derivative of an Inverse Function Copyright © Houghton Mifflin Company. All rights reserved. 16

Definition of the Natural Exponential Function and Figure 5. 19 Copyright © Houghton Mifflin Company. All rights reserved. 17

Theorem 5. 10 Operations with Exponential Functions Copyright © Houghton Mifflin Company. All rights reserved. 18

Properties of the Natural Exponential Function Copyright © Houghton Mifflin Company. All rights reserved. 19

Theorem 5. 11 Derivative of the Natural Exponential Function Copyright © Houghton Mifflin Company. All rights reserved. 20

Theorem 5. 12 Integration Rules for Exponential Functions Copyright © Houghton Mifflin Company. All rights reserved. 21

Definition of Exponential Function to Base a Copyright © Houghton Mifflin Company. All rights reserved. 22

Definition of Logarithmic Function to Base a Copyright © Houghton Mifflin Company. All rights reserved. 23

Properties of Inverse Functions Copyright © Houghton Mifflin Company. All rights reserved. 24

Theorem 5. 13 Derivatives for Bases Other Than e Copyright © Houghton Mifflin Company. All rights reserved. 25

Theorem 5. 14 The Power Rule for Real Exponents Copyright © Houghton Mifflin Company. All rights reserved. 26

Theorem 5. 15 A Limit Involving e Copyright © Houghton Mifflin Company. All rights reserved. 27

Summary of Compound Interest Formulas Copyright © Houghton Mifflin Company. All rights reserved. 28

Definitions of Inverse Trigonometric Functions Copyright © Houghton Mifflin Company. All rights reserved. 29

Figure 5. 29 Copyright © Houghton Mifflin Company. All rights reserved. 30

Properties of Inverse Trigonometric Functions Copyright © Houghton Mifflin Company. All rights reserved. 31

Theorem 5. 16 Derivatives of Inverse Trigonometric Functions Copyright © Houghton Mifflin Company. All rights reserved. 32

Basic Differentiation Rules for Elementary Functions Copyright © Houghton Mifflin Company. All rights reserved. 33

Theorem 5. 17 Integrals Involving Inverse Trigonometric Functions Copyright © Houghton Mifflin Company. All rights reserved. 34

Basic Integration Rules (a > 0) Copyright © Houghton Mifflin Company. All rights reserved. 35

Definitions of the Hyperbolic Functions Copyright © Houghton Mifflin Company. All rights reserved. 36

Figure 5. 37 Copyright © Houghton Mifflin Company. All rights reserved. 37

Hyperbolic Identities Copyright © Houghton Mifflin Company. All rights reserved. 38

Theorem 5. 18 Derivatives and Integrals of Hyperbolic Functions Copyright © Houghton Mifflin Company. All rights reserved. 39

Theorem 5. 19 Inverse Hyperbolic Functions Copyright © Houghton Mifflin Company. All rights reserved. 40

Figure 5. 41 Copyright © Houghton Mifflin Company. All rights reserved. 41

Theorem 5. 20 Differentiation and Integration Involving Inverse Hyperbolic Functions Copyright © Houghton Mifflin Company. All rights reserved. 42