| Introduction |
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PART 1 PRE-CALCULUS REVIEW |
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5 | (36) |
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Chapter 1 Getting Down to Basics: Algebra and Geometry |
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7 | (18) |
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7 | (2) |
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Misc. Algebra: You Know, Like Miss South Carolina |
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9 | (2) |
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Geometry: When Am I Ever Going to Need It? |
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11 | (5) |
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Solutions for This Easy, Elementary Stuff |
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16 | (9) |
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Chapter 2 Funky Functions and Tricky Trig |
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25 | (16) |
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Figuring Out Your Functions |
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25 | (4) |
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Trigonometric Calisthenics |
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29 | (4) |
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Solutions to Functions and Trigonometry |
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33 | (8) |
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PART 2 LIMITS AND CONTINUITY |
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41 | (36) |
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Chapter 3 A Graph Is Worth a Thousand Words: Limits and Continuity |
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43 | (10) |
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Digesting the Definitions: Limit and Continuity |
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44 | (2) |
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Taking a Closer Look: Limit and Continuity Graphs |
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46 | (4) |
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Solutions for Limits and Continuity |
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50 | (3) |
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Chapter 4 Nitty-Gritty Limit Problems |
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53 | (24) |
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Solving Limits with Algebra |
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54 | (5) |
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Pulling Out Your Calculator: Useful "Cheating" |
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59 | (2) |
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Making Yourself a Limit Sandwich |
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61 | (2) |
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Into the Great Beyond: Limits at Infinity |
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63 | (4) |
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Solutions for Problems with Limits |
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67 | (10) |
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77 | (114) |
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Chapter 5 Getting the Big Picture: Differentiation Basics |
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79 | (10) |
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The Derivative: A Fancy Calculus Word for Slope and Rate |
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79 | (2) |
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The Handy-Dandy Difference Quotient |
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81 | (3) |
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Solutions for Differentiation Basics |
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84 | (5) |
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Chapter 6 Rules, Rules, Rules: The Differentiation Handbook |
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89 | (28) |
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89 | (3) |
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Giving It Up for the Product and Quotient Rules |
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92 | (2) |
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Linking Up with the Chain Rule |
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94 | (4) |
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What to Do with Y's: Implicit Differentiation |
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98 | (3) |
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Getting High on Calculus: Higher Order Derivatives |
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101 | (2) |
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Solutions for Differentiation Problems |
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103 | (14) |
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Chapter 7 Analyzing Those Shapely Curves with the Derivative |
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117 | (30) |
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The First Derivative Test and Local Extrema |
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117 | (3) |
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The Second Derivative Test and Local Extrema |
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120 | (2) |
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Finding Mount Everest: Absolute Extrema |
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122 | (4) |
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Smiles and Frowns: Concavity and Inflection Points |
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126 | (3) |
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The Mean Value Theorem: Go Ahead, Make My Day |
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129 | (2) |
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Solutions for Derivatives and Shapes of Curves |
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131 | (16) |
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Chapter 8 Using Differentiation to Solve Practical Problems |
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147 | (26) |
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Optimization Problems: From Soup to Nuts |
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147 | (3) |
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Problematic Relationships: Related Rates |
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150 | (3) |
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A Day at the Races: Position, Velocity, and Acceleration |
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153 | (4) |
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Solutions to Differentiation Problem Solving |
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157 | (16) |
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Chapter 9 Even More Practical Applications of Differentiation |
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173 | (18) |
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Make Sure You Know Your Lines: Tangents and Normals |
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173 | (4) |
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Looking Smart with Linear Approximation |
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177 | (2) |
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Calculus in the Real World: Business and Economics |
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179 | (4) |
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Solutions to Differentiation Problem Solving |
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183 | (8) |
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PART 4 INTEGRATION AND INFINITE SERIES |
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191 | (118) |
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Chapter 10 Getting into Integration |
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193 | (20) |
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Adding Up the Area of Rectangles: Kid Stuff |
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193 | (3) |
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Sigma Notation and Riemann Sums: Geek Stuff |
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196 | (4) |
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Close Isn't Good Enough: The Definite Integral and Exact Area |
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200 | (2) |
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Finding Area with the Trapezoid Rule and Simpson's Rule |
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202 | (3) |
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Solutions to Getting into Integration |
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205 | (8) |
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Chapter 11 Integration: Reverse Differentiation |
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213 | (16) |
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The Absolutely Atrocious and Annoying Area Function |
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213 | (3) |
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Sound the Trumpets: The Fundamental Theorem of Calculus |
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216 | (3) |
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Finding Antiderivatives: The Guess-and-Check Method |
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219 | (2) |
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The Substitution Method: Pulling the Switcheroo |
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221 | (4) |
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Solutions to Reverse Differentiation Problems |
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225 | (4) |
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Chapter 12 Integration Rules for Calculus Connoisseurs |
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229 | (26) |
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Integration by Parts: Here's How u du It |
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229 | (4) |
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Transfiguring Trigonometric Integrals |
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233 | (2) |
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Trigonometric Substitution: It's Your Lucky Day! |
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235 | (2) |
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Partaking of Partial Fractions |
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237 | (4) |
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Solutions for Integration Rules |
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241 | (14) |
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Chapter 13 Who Needs Freud? Using the Integral to Solve Your Problems |
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255 | (22) |
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Finding a Function's Average Value |
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255 | (1) |
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Finding the Area between Curves |
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256 | (2) |
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Volumes of Weird Solids: No, You're Never Going to Need This |
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258 | (7) |
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Arc Length and Surfaces of Revolution |
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265 | (3) |
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Solutions to Integration Application Problems |
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268 | (9) |
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Chapter 14 Infinite (Sort of) Integrals |
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277 | (10) |
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Getting Your Hopes Up with L'Hopital's Rule |
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278 | (2) |
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Disciplining Those Improper Integrals |
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280 | (3) |
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Solutions to Infinite (Sort of) Integrals |
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283 | (4) |
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Chapter 15 Infinite Series: Welcome to the Outer Limits |
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287 | (22) |
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287 | (2) |
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Testing Three Basic Series |
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289 | (2) |
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Apples and Oranges ... and Guavas: Three Comparison Tests |
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291 | (4) |
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Ratiocinating the Two "R" Tests |
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295 | (2) |
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He Loves Me, He Loves Me Not: Alternating Series |
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297 | (2) |
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Solutions to Infinite Series |
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299 | (10) |
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309 | (10) |
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Chapter 16 Ten Things about Limits, Continuity, and Infinite Series |
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311 | (4) |
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311 | (2) |
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First 3 over the "1": 3 parts to the definition of a limit |
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312 | (1) |
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Fifth 3 over the "1": 3 cases where a limit fails to exist |
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312 | (1) |
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Second 3 over the "1": 3 parts to the definition of continuity |
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312 | (1) |
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Fourth 3 over the "1": 3 cases where continuity fails to exist |
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312 | (1) |
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Third 3 over the "m": 3 cases where a derivative fails to exist |
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313 | (1) |
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313 | (2) |
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First 1: The nth term test of divergence |
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313 | (1) |
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Second 1: The nth term test of convergence for alternating series |
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313 | (1) |
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First 3: The three tests with names |
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313 | (1) |
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Second 3: The three comparison tests |
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314 | (1) |
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The 2 in the middle: The two R tests |
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314 | (1) |
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Chapter 17 Ten Things You Better Remember about Differentiation |
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315 | (4) |
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315 | (1) |
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The First Derivative Is a Rate |
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315 | (1) |
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The First Derivative Is a Slope |
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316 | (1) |
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Extrema, Sign Changes, and the First Derivative |
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316 | (1) |
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The Second Derivative and Concavity |
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316 | (1) |
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Inflection Points and Sign Changes in the Second Derivative |
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316 | (1) |
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317 | (1) |
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317 | (1) |
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317 | (1) |
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"PSST," Here's a Good Way to Remember the Derivatives of Trig Functions |
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317 | (2) |
| Index |
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