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| Calculus Subjects | |
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| Chapter? | |
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| Review of Basics | |
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| Numbers and Their Disguises | |
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| Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, intervals? | |
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| Circles, Parabolas, etc | |
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| Completing the Square | |
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| Completing the square in one and two variables? | |
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| Equations | |
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| Solving Equations | |
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| Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property? | |
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| Algebraic | |
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| Functions and Graphs | |
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| Functions and Their Graphs | |
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| Introduction, equations of lines, power functions, shifting graphs, intersection of curves? | |
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| Transcendental Functions | |
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| Cyclic Phenomena: The Six Basic Trigonometric Functions | |
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| Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas | |
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| Exponential Functions | |
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| The family of exponentials, the function | |
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| Composition and Inverse Functions | |
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| Composite functions, the idea of inverses, finding an inverse of f given by a graph, finding the inverse of f given by an expression | |
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| Logarithmic Functions | |
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| Definition of logarithms, logs as inverses of exponential functions, laws of logarithms, the natural logarithm | |
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| Inverse Trigonometric Functions | |
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| The definition of arcsin x, the functions arctan x and arcsec x, inverse trigonometric identities? | |
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| Limits | |
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| Changing the Form of a Function | |
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| Factoring, canceling, long division, rationalizing, extracting a factor from under a root? | |
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| Derivatives | |
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| Simplifying Algebraic Expressions | |
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| Working with difference quotients and rational functions, canceling common factors, rationalizing expressions? | |
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| The Chain Rule | |
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| Decomposition of Functions | |
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| Inner, outer, and outermost functions, decomposing composite functions? | |
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| Implicit Differentiation | |
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| Equations of Degree 1 Revisited | |
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| Solving linear equations involving derivatives? | |
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| Related Rates | |
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| Word Problems, Algebraic and Transcendental | |
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| Applied Max-Min Problems | |
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| Algebraic word problems, the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines, exponential growth and decay? | |
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| Integrating Trigonometric Functions | |
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| Trigonometric Identitie? | |
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| Rewriting trigonometric expressions using identities | |
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| Appendices | |
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| The Binomial Theorem | |
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| Derivation of The Quadratic Formula | |
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| Answers to Exercises | |
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| Index | |