Chapter 1 Limits and Their Properties. Copyright © Houghton Mifflin Company. All rights reserved.1...

Chapter 1Limits and

Their Properties

Copyright © Houghton Mifflin Company. All rights reserved. 1 | 2

Figure 1.1: Definitionof the Slope of a Line


Figure 1.2: Slope of a Line


Figure 1.3: Equations of Lines


Figure 1.1:The Slope-Intercept Equation of a Line


Summary of Equations of Lines


Figure 1.8: Paralleland Perpendicular Lines


Figure 1.11: Definition of aReal-Valued Function of a Real Variable


Figure 1.14: Graph of a Function


Figure 1.15: Vertical Line Test


Figure 1.16: Graphsof Eight Basic Functions


Figure 1.17:Transformation of Functions


Basic Types of Transformations


Figure 1.18: Leading Coefficient Test


Figure 1.19: Definitionof Composite Functions


Figure 1.21: Definitionof Inverse Functions


Figure 1.23: ReflectiveProperty of Inverse Functions


Figure 1.24: Horizontal Line Test


Finding an Inverse Function


Definition of InverseTrigonometric Functions


Figure 1.29: Graphs ofInverse Trigonometric Functions


Properties of InverseTrigonometric Functions


Definition of theNatural Logarithmic Function


Figure 1.46: Definition of a Limit


A Strategy for Finding Limits


The Squeeze Theorem


Figure 1.59: Continuity at aPoint and on an Open Interval


Definition of Continuity


Figure 1.60: Discontinuities


Definition of Continuityon a Closed Interval


Figures 1.69 and 1.70:The Intermediate Value Theorem


Figure 1.74: Definitionof Infinite Limits


Definition of Infinite Limits (cont'd)


Properties of Infinite Limits

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