150notes - Calculus I with Review Differential Calculus Lecture Notes Veselin Jungic& Jamie Mulholland Department of Mathematics Simon Fraser

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Unformatted text preview: Calculus I with Review Differential Calculus Lecture Notes Veselin Jungic & Jamie Mulholland Department of Mathematics Simon Fraser University c Jungic/Mulholland, August 18, 2011 License is granted to print this document for personal/educational use. Contents Contents i Preface iii Greek Alphabet v 1 Review: Functions and Models 1 1.1 Four Ways to Define a Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Mathematical Models: A Catalog of Essential Functions . . . . . . . . . . . . . . . . . . . . . 9 1.3 New Functions From Old Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4 Exponential Functions & Inverse Functions and Logarithms . . . . . . . . . . . . . . . . . . . 23 Review: Preparation for Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2 Limits and Derivatives 37 2.1 The Tangent and Velocity Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2 The Limit of a Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3 Calculating Limits Using the Limit Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4 The Precise Definition of Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.5 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.6 Limits at Infinity: Horizontal Asymptotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Review: Problem Solving and Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.7 Derivatives and Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 2.8 The Derivative as a Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3 Differentiation Rules 89 3.1 Derivatives of Polynomials and Exponential Functions . . . . . . . . . . . . . . . . . . . . . . 90 3.2 The Product and Quotient Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 3.3 Derivatives of Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.4 Chain Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.5 Implicit Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 i ii CONTENTS 3.6 Derivatives of Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.7 Rates of Change in the Natural and Social Sciences . . . . . . . . . . . . . . . . . . . . . . . . 120 3.8 Exponential Growth and Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Review: Preparation for Related Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 3.9 Related rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3....
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This note was uploaded on 12/10/2011 for the course MATH 150 taught by Professor Mohollund during the Fall '08 term at Simon Fraser.

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150notes - Calculus I with Review Differential Calculus Lecture Notes Veselin Jungic& Jamie Mulholland Department of Mathematics Simon Fraser

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