Logarithmic, Exponential, and Other Transcendental Functions

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Presentation transcript:

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.

Theorem 5.1 Properties of the Natural Logarithmic Function Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.2 Logarithmic Properties Copyright © Houghton Mifflin Company. All rights reserved.

Definition of e and Figure 5.5 Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.3 Derivative of the Natural Logarithmic Function Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.4 Derivative Involving Absolute Value Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.5 Log Rule for Integration Copyright © Houghton Mifflin Company. All rights reserved.

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

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

Definition of Inverse Function and Figure 5.10 Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.6 Reflective Property of Inverse Functions and Figure 5.12 Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.7 The Existence of an Inverse Function and Figure 5.13 Copyright © Houghton Mifflin Company. All rights reserved.

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

Theorem 5.8 Continuity and Differentiability of Inverse Functions Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.9 The Derivative of an Inverse Function Copyright © Houghton Mifflin Company. All rights reserved.

Definition of the Natural Exponential Function and Figure 5.19 Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.10 Operations with Exponential Functions Copyright © Houghton Mifflin Company. All rights reserved.

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

Theorem 5.11 Derivative of the Natural Exponential Function Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.12 Integration Rules for Exponential Functions Copyright © Houghton Mifflin Company. All rights reserved.

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

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

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

Theorem 5.13 Derivatives for Bases Other Than e Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.14 The Power Rule for Real Exponents Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.15 A Limit Involving e Copyright © Houghton Mifflin Company. All rights reserved.

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

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

Figure 5.29 Copyright © Houghton Mifflin Company. All rights reserved.

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

Theorem 5.16 Derivatives of Inverse Trigonometric Functions Copyright © Houghton Mifflin Company. All rights reserved.

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

Theorem 5.17 Integrals Involving Inverse Trigonometric Functions Copyright © Houghton Mifflin Company. All rights reserved.

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

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

Figure 5.37 Copyright © Houghton Mifflin Company. All rights reserved.

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

Theorem 5.18 Derivatives and Integrals of Hyperbolic Functions Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.19 Inverse Hyperbolic Functions Copyright © Houghton Mifflin Company. All rights reserved.

Figure 5.41 Copyright © Houghton Mifflin Company. All rights reserved.

Theorem 5.20 Differentiation and Integration Involving Inverse Hyperbolic Functions Copyright © Houghton Mifflin Company. All rights reserved.