# Math 180 - Calculus I

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 ​ Chapter 1: Functions and Models Section Topic 1.1 Four Ways to Represent a Function​ 1.2 Mathematical Models: A Catalog of Essential Functions1.2.20 Mathematical Models 1.3 New Functions from Old Functions1.3.46 New Functions from Old Functions1.3.50 New Functions from Old Functions 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms1.5.54 Inverse Functions and Logarithms1.5.62 Inverse Functions and Logarithms Chapter 2: Limits and Derivatives Section Topic 2.1 The Tangent and Velocity Problems 2.2 The Limit of a Function2.2.12 The Limit of a Function2.2.20 The Limit of a Function2.2.30 The Limit of a Function2.2.50 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws2.3.26 Calculating Limits Using the Limit Laws2.3.32 Calculating Limits Using the Limit Laws2.3.56 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit2.4.12 The Precise Definition of a Limit2.4.22 The Precise Definition of a Limit2.4.28 The Precise Definition of a Limit 2.5 Continuity2.5.14 Continuity2.5.34 Continuity2.5.60 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes2.6.24 Limits at Infinity; Horizontal Asymptotes2.6.46 Limits at Infinity; Horizontal Asymptotes2.6.68 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change2.7.14 Derivatives and Rates of Change2.7.48 Derivatives and Rates of Change2.7.56 Derivatives and Rates of Change 2.8 The Derivative as a Function2.8.12 The Derivative as a Function2.8.38 The Derivative as a Function2.8.58 The Derivative as a Function Chapter 3: Differentiation Rules Section Topic 3.1 Derivatives of Polynomial and Exponential Functions3.1.22 Derivatives of Polynomial and Exponential Functions3.1.28 Derivatives of Polynomial and Exponential Functions3.1.50 Derivatives of Polynomial and Exponential Functions3.1.54 Derivatives of Polynomial and Exponential Functions3.1.70 Derivatives of Polynomial and Exponential Functions 3.2 The Product and Quotient Rules​3.2.16 The Product and Quotient Rules3.2.24 The Product and Quotient Rules3.2.36 The Product and Quotient Rules3.2.60 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions3.3.12 Derivatives of Trigonometric Functions3.3.26 Derivatives of Trigonometric Functions3.3.36 Derivatives of Trigonometric Functions 3.4 The Chain Rule3.4.26 The Chain Rule3.4.38 The Chain Rule3.4.50 The Chain Rule3.4.84 The Chain Rule 3.5 Implicit Differentiation3.5.18 Implicit Differentiation3.5.30 Implicit Differentiation3.5.42 Implicit Differentiation3.5.58 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions3.6.20 Derivatives of Logarithmic Functions3.6.26 Derivatives of Logarithmic Functions3.6.44 Derivatives of Logarithmic Functions 3.7 Rates of Change in the Natural and Social Sciences3.7.26 Rates of Change in the Natural Sciences 3.8 Exponential Growth and Decay3.8.8 Exponential Growth and Decay3.8.16 Exponential Growth and Decay3.8.20 Exponential Growth and Decay 3.9 Related Rates3.9.16 Related Rates3.9.20 Related Rates3.9.26 Related Rates3.9.44 Related Rates3.9.50 Related Rates 3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions3.11.23 Hyperbolic Functions3.11.54 Hyperbolic Functions Chapter 4: Applications of Differentiation Section Topic 4.1 Maximum and Minimum Values4.1.36 Maximum and Minimum Values4.1.42 Maximum and Minimum Values4.1.60 Maximum and Minimum Values4.1.72 Maximum and Minimum Values 4.2 The Mean Value Theorem 4.3 How Derivatives Affect the Shape of a Graph4.3.14 How Derivatives Affect the Shape of a Graph4.3.44 How Derivatives Affect the Shape of a Graph4.3.72 How Derivatives Affect the Shape of a Graph 4.4 Indeterminate Forms and l’Hospital’s Rule4.4.26 Indeterminate Forms and l'Hospital's Rule4.4.52 Indeterminate Forms and l'Hospital's Rule4.4.64 Indeterminate Forms and l'Hospital's Rule4.4.78 Indeterminate Forms and l'Hospital's Rule 4.5 Summary of Curve Sketching 4.6 Graphing With Calculus and Calculators 4.7 Optimization Problems4.7.32 Optimization Problems4.7.46 Optimization Problems4.7.64 Optimization Problems4.7.DrH-01 Optimization Problems 4.8 Newton’s Method 4.9 Antiderivatives​4.9.42 Antiderivatives4.9.46 Antiderivatives Chapter 5: Integrals Section Topic 5.1 Areas and Distances5.1.6 Areas and Distances5.1.20 Areas and Distances5.1.31 Areas and Distances 5.2 The Definite Integral5.2.20 The Definite Integral5.2.24 The Definite Integral5.2.39 The Definite Integral 5.3 The Fundamental Theorem of Calculus5.3.2 The Fundamental Theorem of Calculus5.3.12 The Fundamental Theorem of Calculus5.3.18 The Fundamental Theorem of Calculus5.3.28 The Fundamental Theorem of Calculus5.3.42 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem5.4.6 Indefinite Integrals and the Net Change Theorem5.4.14 Indefinite Integrals and the Net Change Theorem5.4.28 Indefinite Integrals and the Net Change Theorem5.4.40 Indefinite Integrals and the Net Change Theorem5.4.50 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule​​5.5.22 The Substitution Rule5.5.24 The Substitution Rule5.5.56 The Substitution Rule5.5.66 The Substitution Rule5.5.84 The Substitution Rule
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