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Tables of Contents for Discovering Calculus With the Graphing Calculator
Chapter/Section Title
Page #
Page Count
Pitfalls in Using Technology
xi
Chapter 1 Functions and Graphs--A Review
1
16
Graphs of Inequalities
1
4
Graphs of Absolute Values
5
4
Slope, y-Intercepts, and the Equaions of Lines
9
4
Distance
13
2
Equations of the Form ax2 + bx + c
15
2
Chapter 2 Limits and Continuity
17
26
Zeros, Domain, and Range
17
4
Odd and Even Functions
21
2
The Concept of Limit
23
4
One-Sided and Two-Sided Limits
27
4
Defining Limits Formally With Delta and Epsilon by Examining Input/Output Values
31
4
Continuity
35
4
Limits and Continuity of Trigonometric Functions
39
4
Chapter 3 Differentiation
43
20
Secant Lines and Tangent Lines
43
6
The Difference Quotient and Estimating the Derivative of a Function
49
4
Derivatives That Fail to Exist
53
4
Differentiation Rules
57
2
Velocity and Speed--An Exploration in Parametric Mode Vertical and Horizontal Motion on the Graphing Calculator
59
4
Chapter 4 Applications of the Derivative
63
22
Discovering the Relationship Between a Function and its Derivative
63
2
The First Derivative Test and Intervals of Increasing and Decreasing
65
4
The First Derivative Test and Maxima and Minima
69
4
The Second Derivative Test and Concavity
73
2
Curve Sketching
75
6
Volume of a Cone
81
2
Newton's Method
83
2
Chapter 5 Integration
85
12
Antiderivatives: The Indefinite Integral
85
2
Area and Riemann Sums as a Function of the Number of Subintervals
87
4
The Fundamental Theorem of Calculus
91
4
Integration by Substitution
95
2
Chapter 6 Applications of the Definite Integral
97
14
Area Between Two Curves
97
4
Volume
101
4
Arc Length and Surface Area
105
4
Applications of Integration to Rectilinear Motion
109
2
Chapter 7 Logarithmic and Exponential Functions
111
22
Inverse Functions
111
6
Graphs of y = 1nx and y = ex
117
4
Developing the Log Identity Rules Graphically Solving Equations Involoving Logs
121
4
Derivatives and Integrals of Logarithmic and Exponential Functions
125
4
Hyperbolic Functions--Identities, Derivatives, and Integrals
129
4
Chapter 8 Inverse Trigonometric Functions and Inverse Hyperbolic Functions
133
12
Inverse Trigonometric Functions
133
4
Derivatives and Integrals of Inverse Trigonometric Functions
137
4
Inverse Hyperbolic Functions--Derivatives and Integrals of Inverse Hyperbolic Functions
141
4
Chapter 9 Techniques of Integration
145
14
Integration by Parts
145
4
Integrals of Trigonometric Functions
149
2
Trigonometric Substitutions
151
2
Integrating Rational Functions Using Partial Fraction Decomposition
153
2
Trapezoidal Rule and Simpson's Rule
155
4
Chapter 10 Improper Integrals and L 'Hopital's Rule
159
8
Visually Exploring the Graphs of y = f(x)/g(x) and y = f'(x)/g'(x)
159
2
Improper Integrals
161
4
L'Hopital's Rule
165
2
Chapter 11 Infinite Series
167
12
Sequences and Their Limits
167
4
Tests of Convergence
171
2
Alternating Series
173
2
Taylor and Maclaurin Series
175
4
Chapter 12 Conic Sections
179
12
Parabolas
179
4
Ellipses
183
4
Hyperbolas
187
2
Parametrizations of Plane Curves
189
2
Chapter 13 Polar Coordinates and Parametric Equations
191
Exploring Graphs in Polar Coordinates
191
4
Converting Rectangular Graphs into Polar Graphs
195
2
Points of Intersection in Polar Coordinates
197
2
Area in Polar Coordinates
199
2
Parametric Equations
201
2
Tangent Lines and Arc Length in Polar Coordinates
203