03831 2200157 4500245007500000020002200075250000600097100002000103650001300123005001900136260003200155041001200187084000800199300003800207500342800245 aCalculus. Early Transcendental Functions. Single Variable 3edhPrinted a978-0-07-287030-5 a3 aSMITH, Robert T aKalkulus a20151223074040 aNew YorkbMcGraw-Hillc2007 aEnglish a515 axxxii, 851 hal. :bilus. ;c26 cm aCHAPTER 0 PRELIMINARIES..10.1 Polynominals and Rational Functions..20.2 Graphing Calculators and Computer Algebra Systems..200.3 Inverse Functions..290.4 Trigonometric and Inverse Trigonometric Functions..360.5 Exponential and Logarithmic Functions..480.6 Transformations of Functions..61CHAPTER 1 LIMITS AND CONTINUITY..731.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve..741.2 The Concept of Limit..791.3 Computation of Limits..871.4 Continuity and Its Consequences..971.5 Limits Involving Infinity..1101.6 Formal Definition of the Limit..1211.7 Limits and Loss-of-Significance Errors..134CHAPTER 2 DIFFERENTIATION..1452.1 Tangent Lines and Velocity..1462.2 The Derivative..1592.3 Computatin of Derivatives: The Power Rule..1702.4 The Product and Quotient Rules..1802.5 The Chain Rule..1892.6 Derivatives of Trigonometric Functions..1862.7 Derivatives of Exponential and Logarithmic Functions..2062.8 Implicit Differentiation and Inverse Trigonometric Function..2162.9 The Mean Value Theorem..226CHAPTER 3 APPLICATIONS OF DIFFERENTIATION..2413.1 Linear Approximations and Newton's Method..2423.2 Indeterminate Forms and L'Hospital's Rule..2553.3 Maximum and Minimum Values..2653.4 Increasing and Decreasing Functions..2773.5 Concavity and the Second Derivative Test..2863.6 Overview of Curve Sketching..2963.7 Optimization..3083.8 Related Rates..3213.9 Rates of Change in Economics and the Sciences..327CHAPTER 4 INTEGRATION..3434.1 Antiderivatives..3444.2 Sums and Sigma Notation..3544.3 Area..3624.4 The Definite Integral..3694.5 The Fundamental Theorem of Calculus..3834.6 Integration by Substitution..3934.7 Numerical Integration..4024.8 The Natural Logarithm as an Integral..416CHAPTER 5 APPLICATIONS OF THE DEFINITE INTEGRAL..4315.1 Area Between Curves..4325.2 Volume: Slicing, Disks, and Washers..4415.3 Volumes by Cylindrical Shells..4565.4 Arc Length and Surface Area..4645.5 Projectile Motion..4725.6 Applications of Integration to Physics and Engineering..4845.7 Probability..496CHAPTER 6 INTEGRATION TECHNIQUES..5096.1 Review of Formulas and Techniques..5106.2 Integration by Parts..5146.3 Trigonometric Techniques of Integration..5216.4 Integration of Rational Function Using Partial Fractions..5306.5 Integration Tables and Computer Algebra Systems..5386.6 Improper Integrals..546CHAPTER 7 FIRST-ORDER DIFFERENTIAL EQUATIONS..5657.1 Modelling with Differential Equations..5667.2 Separable Differential Equations..5777.3 Direction Fields and Euler's Method..5877.4 Systems of First-Order Differential Equations..599CHAPTER 8 INFINITE SERIES..6118.1 Sequances of Real Numbers..6128.2 Infinite Series..6268.3 The Integral Test and Comparison Tests..6368.4 Alternating Series..6488.5 Absolute Convergence and the Ratio Test..6568.6 Power Series..6648.7 Taylor Series..6728.8 Applications of Taylor Series..6858.9 Fourier Series..694CHAPTER 9 PARAMETRIC EQUATIONS AND POLAR COORDINATES..7159.1 Plane Curves and parametric Equations..7169.2 Calculus and Parametric Equations..7269.3 Arc Length and Surface Area in Parametric Equations..7349.4 Polar Coordinates..7429.5 Calculus and Polar Coordinates..7559.6 Conic Secions..7649.7 Conic Sections in Polar Coordinates..774CHAPTER 10 VECTORS AND THE GEOMETRY OF SPACE..78510.1 Vectors in the Plane..78610.2 Vectors in Space..79610.3 The Dot Product..80410.4 The Cross Product..81510.5 Lines and Planes in Space..82810.6 Surfaces in Space..837