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Calculus Lab Manual
MTH 251 at Portland Community College
Steve Simonds, Alex Jordan (Editor)
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Front Matter
Colophon
Acknowledgements
To All
To the Student
To the Instructor
1
Rates Of Change
1.1
Velocity
1.1
Exercises
1.2
Secant Line to a Curve
1.2
Exercises
1.3
The Difference Quotient
1.3
Exercises
1.4
Supplement
2
Limits and Continuity
2.1
Limits
2.1
Exercises
2.2
Limit Laws
2.2
Exercises
2.3
Indeterminate Limits
2.3
Exercises
2.4
Limits at Infinity
2.4
Exercises
2.5
Limits at Infinity Tending to Zero
2.5
Exercises
2.6
Ratios of Infinities
2.6
Exercises
2.7
Non-existent Limits
2.7
Exercises
2.8
Vertical Asymptotes
2.8
Exercises
2.9
Continuity
2.9
Exercises
2.10
Discontinuities
2.10
Exercises
2.11
Continuity on an Interval
2.11
Exercises
2.12
Discontinuous Formulas
2.12
Exercises
2.13
Piecewise-Defined Functions
2.13
Exercises
2.14
Supplement
3
Introduction to the First Derivative
3.1
Instantaneous Velocity
3.1
Exercises
3.2
Tangent Lines
3.2
Exercises
3.3
The First Derivative
3.3
Exercises
3.4
Derivative Units
3.4
Exercises
3.5
Supplement
4
Functions, Derivatives, and Antiderivatives
4.1
Graph Features
4.1
Exercises
4.2
Graphical Derivatives
4.2
Exercises
4.3
Nondifferentiability
4.3
Exercises
4.4
Higher Order Derivatives
4.4
Exercises
4.5
Antiderivatives
4.5
Exercises
4.6
Graphical Features from Derivatives
4.6
Exercises
4.7
Supplement
5
Derivative Formulas
5.1
Leibniz Notation
5.1
Exercises
5.2
The Derivative Operator
5.2
Exercises
5.3
The Power Rule
5.3
Exercises
5.4
The Constant Factor Rule
5.4
Exercises
5.5
The Constant Divisor Rule
5.5
Exercises
5.6
The Sum and Difference Rules
5.6
Exercises
5.7
The Product Rule
5.7
Exercises
5.8
The Quotient Rule
5.8
Exercises
5.9
Simplification
5.9
Exercises
5.10
Product and Quotient Rules Together
5.10
Exercises
5.11
Derivative Formulas and Function Behavior
5.11
Exercises
5.12
Supplement
6
The Chain Rule
6.1
Introduction to the Chain Rule
6.1
Exercises
6.2
Order to Apply Rules
6.2
Exercises
6.3
Not Simplifying First
6.3
Exercises
6.4
Chain Rule with Leibniz Notation
6.4
Exercises
6.5
Supplement
7
Implicit Differentiation
7.1
General Implicit Differentiation
7.1
Exercises
7.2
Derivatives of Inverse Functions
7.2
Exercises
7.3
Logarithmic Differentiation
7.3
Exercises
7.4
Supplement
7.4
Exercises
8
Related Rates
Introduction
8.1
Introduction to Related Rates
8.1
Exercises
8.2
Diagrams for Related Rates
8.2
Exercises
8.3
Supplement
9
Critical Numbers and Graphing from Formulas
9.1
Motivation
9.1
Exercises
9.2
Local Extrema
9.2
Exercises
9.3
Formal Identification of Critical Numbers
9.3
Exercises
9.4
Sign Tables for the First Derivative
9.4
Exercises
9.5
Inflection Points
9.5
Exercises
9.6
End Behavior
9.6
Exercises
9.7
Making Graphs
9.7
Exercises
9.8
Supplement
Appendices
A.
Limit Laws
B.
Derivative Formulas
C.
Some Useful Rules of Algebra
D.
Units of Measure
E.
Solutions to Supplemental Exercises
Colophon
Colophon
Website
spot.pcc.edu/math/clm
©2012–2016 Portland Community College
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
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