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| Functions | |
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| Functions | |
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| Graphing Functions Using Calculators and Computer Algebra Systems | |
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| New Functions from Old | |
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| Families of Functions | |
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| Inverse Functions Inverse Trigonometric Functions | |
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| Exponential and Logarithmic Functions | |
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| Mathematical Models | |
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| Parametric Equations 86 | |
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| Limits And Continuity | |
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| Limits (An Intuitive Approach) | |
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| Computing Limits | |
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| Limits at Infinity End Behavior of a Function | |
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| Limits (Discussed More Rigorously) | |
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| Continuity | |
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| Continuity of Trigonometric and Inverse Functions | |
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| The Derivative | |
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| Tangent Lines, Velocity, and General Rates of Change | |
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| The Derivative Function | |
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| Techniques of Differentiation | |
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| The Product and Quotient Rules | |
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| Derivatives of Trigonometric Functions | |
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| The Chain Rule | |
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| Related Rates | |
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| Local Linear Approximation Differentials | |
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| Exponential, Logarithmic, And Inverse Trigonometric Functions | |
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| Implicit Differentiation | |
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| Derivatives of Logarithmic Functions | |
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| Derivatives of Exponential and Inverse Trigonometric Functions | |
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| L'H(pital's Rule Indeterminate Forms | |
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| The Derivative In Graphing And Applications | |
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| Analysis of Functions I: Increase, Decrease, and Concavity | |
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| Analysis of Functions II: Relative Extrema Graphing Polynomials | |
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| More on Curve Sketching: Rational Functions Curves with Cusps and Vertical Tangent Lines Using Technology | |
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| Absolute Maxima and Minima | |
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| Applied Maximum and Minimum Problems | |
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| Newton's Method | |
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| Rolle's Theorem Mean-Value Theorem | |
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| Rectilinear Motion | |
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| Integration | |
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| An Overview of the Area Problem | |
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| The Indefinite Integral | |
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| Integration by Substitution | |
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| The Definition of Area as a Limit Sigma Notation | |
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| The Definite Integral | |
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| The Fundamental Theorem of Calculus | |
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| Rectilinear Motion Revisited Using Integration | |
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| Evaluating Definite Integrals by Substitution | |
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| Applications Of The Definite Integral In Geometry, Science, And Engineering | |
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| Area Between Two Curves | |
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| Volumes by Slicing Disks and Washers | |
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| Volumes by Cylindrical Shells | |
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| Length of a Plane Curve | |
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| Area of a Surface of Revolution | |
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| Average Value of a Function and its Applications | |
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| Work | |
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| Fluid Pressure and Force | |
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| Hyperbolic Functions and Hanging Cables | |
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| Principles Of Integral Evaluation | |
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| An Overview of Integration Methods | |
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| Integration by Parts | |
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| Trigonometric Integrals | |
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| Trigonometric Substitutions | |
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| Integrating Rational Functions by Partial Fractions | |
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| Using Computer Algebra Systems and Tables of Integrals | |
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| Numerical Integration Simpson's Rule | |
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| Improper Integrals | |
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| Mathematical Modeling With Differential Equations | |
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| First-Order Differential Equations and Applications | |
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| Slope Fields Euler's Method | |
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| Modeling with First-Order Differential Equations | |
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| Second-Order Linear Homogeneous Differential Equations The Vibrating Spring | |
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| Infinite Series | |
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| Sequences | |
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| Monotone Sequences | |
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| Infinite Series | |
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| Convergence Tests | |
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| The Comparison, Ratio, and Root Tests | |
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| Alternating | |