Calculus I
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English
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Entries: 83
Paul Dawkins
calculus
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Calculus I
Preparing book pages
1
Entries
83
Review
Theory
Page 11
Introduction
Theory
Page 11
Functions
Theory
Page 13
Inverse Functions
Theory
Page 19
Trig Functions
Theory
Page 26
Solving Trig Equations
Theory
Page 33
Solving Trig Equations with Calculators, Part I
Theory
Page 42
Solving Trig Equations with Calculators, Part II
Theory
Page 53
Exponential Functions
Theory
Page 58
Logarithm Functions
Theory
Page 61
Exponential and Logarithm Equations
Theory
Page 67
Common Graphs
Theory
Page 73
Limits
Theory
Page 85
Introduction
Theory
Page 85
Rates of Change and Tangent Lines
Theory
Page 87
The Limit
Theory
Page 96
One-Sided Limits
Theory
Page 106
Limit Properties
Theory
Page 112
Computing Limits
Theory
Page 118
Infinite Limits
Theory
Page 126
Limits At Infinity, Part I
Theory
Page 135
Limits At Infinity, Part II
Theory
Page 144
Continuity
Theory
Page 153
The Definition of the Limit
Theory
Page 160
Derivatives
Theory
Page 175
Introduction
Theory
Page 175
The Definition of the Derivative
Theory
Page 177
Interpretations of the Derivative
Theory
Page 183
Differentiation Formulas
Theory
Page 188
Product and Quotient Rule
Theory
Page 196
Derivatives of Trig Functions
Theory
Page 202
Derivatives of Exponential and Logarithm Functions
Theory
Page 213
Derivatives of Inverse Trig Functions
Theory
Page 218
Derivatives of Hyperbolic Functions
Theory
Page 224
Chain Rule
Theory
Page 226
Implicit Differentiation
Theory
Page 236
Related Rates
Theory
Page 245
Higher Order Derivatives
Theory
Page 259
Logarithmic Differentiation
Theory
Page 264
Applications of Derivatives
Theory
Page 267
Introduction
Theory
Page 267
Rates of Change
Theory
Page 269
Critical Points
Theory
Page 272
Minimum and Maximum Values
Theory
Page 278
Finding Absolute Extrema
Theory
Page 286
The Shape of a Graph, Part I
Theory
Page 292
The Shape of a Graph, Part II
Theory
Page 301
The Mean Value Theorem
Theory
Page 310
Optimization
Theory
Page 317
More Optimization Problems
Problem
Page 331
Indeterminate Forms and L’Hospital’s Rule
Theory
Page 345
Linear Approximations
Theory
Page 351
Differentials
Theory
Page 354
Newton’s Method
Theory
Page 357
Business Applications
Theory
Page 362
Integrals
Theory
Page 368
Introduction
Theory
Page 368
Indefinite Integrals
Theory
Page 369
Computing Indefinite Integrals
Theory
Page 375
Substitution Rule for Indefinite Integrals
Theory
Page 385
More Substitution Rule
Theory
Page 398
Area Problem
Theory
Page 411
The Definition of the Definite Integral
Theory
Page 421
Computing Definite Integrals
Theory
Page 431
Substitution Rule for Definite Integrals
Theory
Page 443
Applications of Integrals
Theory
Page 454
Introduction
Theory
Page 454
Average Function Value
Theory
Page 455
Area Between Curves
Theory
Page 458
Volumes of Solids of Revolution / Method of Rings
Theory
Page 469
Volumes of Solids of Revolution / Method of Cylinders
Theory
Page 479
Work
Theory
Page 487
Extras
Other
Page 491
Introduction
Theory
Page 491
Proof of Various Limit Properties
Theory
Page 492
Proof of Various Derivative Facts/Formulas/Properties
Theory
Page 503
Proof of Trig Limits
Theory
Page 516
Proofs of Derivative Applications Facts/Formulas/Properties
Theory
Page 521
Proof of Various Integral Facts/Formulas/Properties
Theory
Page 532
Area and Volume Formulas
Theory
Page 544
Types of Infinity
Theory
Page 548
Summation Notation
Theory
Page 552
Constants of Integration
Theory
Page 554
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