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The table of contents for this book is as follows:

Table of Contents iii 1 Limits 1 1.1 An IntroducƟon To Limits . . . . . . . . . . . . . . . . . . . . . 1 1.2 Epsilon-Delta Definition of a Limit . . . . . . . . . . . . . . . . 9 1.3 Finding Limits Analytically . . . . . . . . . . . . . . . . . . . . . 16 1.4 One Sided Limits . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.5 Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.6 Limits involving infinity . . . . . . . . . . . . . . . . . . . . . . 45 2 Derivatives 57 2.1 Instantaneous Rates of Change: The Derivative . . . . . . . . . 57 2.2 Interpretations of the Derivative . . . . . . . . . . . . . . . . . 71 2.3 Basic Differentiation Rules . . . . . . . . . . . . . . . . . . . . 78 2.4 The Product and Quotient Rules . . . . . . . . . . . . . . . . . 85 2.5 The Chain Rule . . . . . . . . . . . . . . . . . . . . . . . . . . 95 2.6 Implicit Differentiation . . . . . . . . . . . . . . . . . . . . . . 105 2.7 Derivatives of Inverse FuncƟons . . . . . . . . . . . . . . . . . 116 3 The Graphical Behavior of Functions 123 3.1 Extreme Values . . . . . . . . . . . . . . . . . . . . . . . . . . 123 3.2 The Mean Value Theorem . . . . . . . . . . . . . . . . . . . . . 131 3.3 Increasing and Decreasing Functions . . . . . . . . . . . . . . . 136 3.4 Concavity and the Second Derivative . . . . . . . . . . . . . . . 144 3.5 Curve Sketching . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4 Applications of the Derivative 159 4.1 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . . 159 4.2 Related Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 4.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 4.4 Differentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Calculus II begins here) 5 Integration 189 5.1 Antiderivatives and Indefinite Integration . . . . . . . . . . . . 189 5.2 The Definite Integral . . . . . . . . . . . . . . . . . . . . . . . 199 5.3 Riemann Sums . . . . . . . . . . . . . . . . . . . . . . . . . . 210 5.4 The Fundamental Theorem of Calculus . . . . . . . . . . . . . . 227 5.5 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . 239 6 Techniques of Antidifferentiation 253 6.1 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 6.2 Integration by Parts . . . . . . . . . . . . . . . . . . . . . . . . 273 6.3 Trigonometric Integrals . . . . . . . . . . . . . . . . . . . . . . 284 6.4 Partial Fraction Decomposition . . . . . . . . . . . . . . . . . . 294 6.5 Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . 302 6.6 L’Hôpital’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . 312 6.7 Improper Integration . . . . . . . . . . . . . . . . . . . . . . . 321 7 Applications of Integration 333 7.1 Area Between Curves . . . . . . . . . . . . . . . . . . . . . . . 334 7.2 Volume by Cross-SetiƟonal Area; Disk and Washer Methods . . . 342 7.3 The Shell Method . . . . . . . . . . . . . . . . . . . . . . . . . 350 7.4 Arc Length and Surface Area . . . . . . . . . . . . . . . . . . . 358 7.5 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 7.6 Fluid Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 8 Sequences and Series 385 8.1 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 8.2 Infinite Series . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 8.3 Taylor Polynomials . . . . . . . . . . . . . . . . . . . . . . . . 414 A Solutions To Selected Problems 

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