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Calculus Lab Manual:
MTH 251 at Portland Community College
Steve Simonds, Alex Jordan (Editor)
Contents
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Contents
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Front Matter
Colophon
Acknowledgements
To All
To the Student
To the Instructor
1
Rates Of Change
Velocity
Secant Line to a Curve
The Difference Quotient
Supplement
2
Limits and Continuity
Limits
Limits Laws
Indeterminate Limits
Limits at Infinity
Limits at Infinity Tending to Zero
Ratios of Infinities
Non-existent Limits
Vertical Asymptotes
Continuity
Discontinuities
Continuity on an Interval
Discontinuous Formulas
Piecewise-Defined Functions
Supplement
3
Introduction to the First Derivative
Instantaneous Velocity
Tangent Lines
The First Derivative
Derivative Units
Supplement
4
Functions, Derivatives, and Antiderivatives
Graph Features
Graphical Derivatives
Nondifferentiability
Higher Order Derivatives
Antiderivatives
Graphical Features from Derivatives
Supplement
5
Derivative Formulas
Leibniz Notation
The Derivative Operator
The Power Rule
The Constant Factor Rule
The Constant Divisor Rule
The Sum and Difference Rules
The Product Rule
The Quotient Rule
Simplification
Product and Quotient Rules Together
Derivative Formulas and Function Behavior
Supplement
6
The Chain Rule
Introduction to the Chain Rule
Order to Apply Rules
Not Simplifying First
Chain Rule with Leibniz Notation
Supplement
7
Implicit Differentiation
General Implicit Differentiation
Derivatives of Inverse Functions
Logarithmic Differentiation
Supplement
8
Related Rates
Introduction to Related Rates
Diagrams for Related Rates
Supplement
9
Critical Numbers and Graphing from Formulas
Motivation
Local Extrema
Formal Identification of Critical Numbers
Sign Tables for the First Derivative
Inflection Points
End Behavior
Making Graphs
Supplement
Appendices
A
Limit Laws
B
Derivative Formulas
C
Some Useful Rules of Algebra
D
Units of Measure
E
Answers to Exercises
Authored in PreTeXt
Calculus Lab Manual:
MTH 251 at Portland Community College
Steve Simonds
Department of Mathematics
Portland Community College
ssimonds@pcc.edu
Alex Jordan, Editor
Department of Mathematics
Portland Community College
alex.jordan@pcc.edu
February 18, 2019
Colophon
Acknowledgements
To All
To the Student
To the Instructor
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