Chapter 5
Logarithmic,
Exponential, and
Other Transcendental
Functions
Definition of the Natural Logarithmic Function
and Figure 5.1
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5-2
Theorem 5.1 Properties of the Natural
Logarithmic Function
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5-3
Theorem 5.2 Logarithmic Properties
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5-4
Definition of e and Figure 5.5
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5-5
Theorem 5.3 Derivative of the Natural
Logarithmic Function
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5-6
Theorem 5.4 Derivative Involving Absolute
Value
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5-7
Theorem 5.5 Log Rule for Integration
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5-8
Guidelines for Integration
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5-9
Integrals of the Six Basic Trigonometric
Functions
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5-10
Definition of Inverse Function and Figure 5.10
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5-11
Theorem 5.6 Reflective Property of Inverse
Functions and Figure 5.12
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5-12
Theorem 5.7 The Existence of an Inverse
Function and Figure 5.13
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5-13
Guidelines for Finding an Inverse Function
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5-14
Theorem 5.8 Continuity and Differentiability of
Inverse Functions
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5-15
Theorem 5.9 The Derivative of an Inverse
Function
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5-16
Definition of the Natural Exponential Function
and Figure 5.19
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5-17
Theorem 5.10 Operations with Exponential
Functions
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5-18
Properties of the Natural Exponential
Function
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5-19
Theorem 5.11 Derivative of the Natural
Exponential Function
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5-20
Theorem 5.12 Integration Rules for
Exponential Functions
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5-21
Definition of Exponential Function to Base a
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5-22
Definition of Logarithmic Function to Base a
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5-23
Properties of Inverse Functions
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5-24
Theorem 5.13 Derivatives for Bases Other
Than e
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5-25
Theorem 5.14 The Power Rule for Real
Exponents
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5-26
Theorem 5.15 A Limit Involving e
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5-27
Summary of Compound Interest Formulas
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5-28
Definitions of Inverse Trigonometric
Functions
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5-29
Figure 5.29
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5-30
Properties of Inverse Trigonometric Functions
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5-31
Theorem 5.16 Derivatives of Inverse
Trigonometric Functions
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5-32
Basic Differentiation Rules for Elementary
Functions
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5-33
Theorem 5.17 Integrals Involving Inverse
Trigonometric Functions
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5-34
Basic Integration Rules (a > 0)
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5-35
Definitions of the Hyperbolic Functions
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5-36
Figure 5.37
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5-37
Hyperbolic Identities
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5-38
Theorem 5.18 Derivatives and Integrals of
Hyperbolic Functions
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5-39
Theorem 5.19 Inverse Hyperbolic Functions
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5-40
Figure 5.41
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5-41
Theorem 5.20 Differentiation and Integration
Involving Inverse Hyperbolic Functions
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5-42