3000 solved problems in Calculus

CONTENTS

Chapter 1 INEQUALITIES 1
Chapter 2 ABSOLUTE VALUE 5
Chapter 3 LINES 9
Chapter 4 CIRCLES 19
Chapter 5 FUNCTIONS AND THEIR GRAPHS 23
Chapter 6 LIMITS 35
Chapter 7 CONTINUITY 43
Chapter 8 THE DERIVATIVE 49
Chapter 9 THE CHAIN RULE 56
Chapter 10 TRIGONOMETRIC FUNCTIONS AND THEIR DERIVATIVES 62
Chapter 11 ROLLE'S THEOREM. THE MEAN VALUE THEOREM. AND THE SIGN OF THE DERIVATIVE 69
Chapter 12 HIGHER-ORDER DERIVATIVES AND IMPLICIT DIFFERENTIATION 75
Chapter 13 MAXIMA AND MINIMA 81
Chapter 14 RELATED RATES 88
Chapter 15 CURVE SKETCHING (GRAPHS) 100
Chapter 16 APPLIED MAXIMUM AND MINIMUM PROBLEMS 118
Chapter 17 RECTILINEAR MOTION 133
Chapter 18 APPROXIMAT ION BY DIFFERENTIALS 138
Chapter 19 ANTIDERIVATIVES (INDEFINITE INTEGRALS) 142
Chapter 20 THE DEFINITE INTEGRAL AND THE FUNDAMENTAL THEOREM OF
CALCULUS 152
Chapter 21 AREA AND ARC LENGTH 163
Chapter 22 VOLUME 173
Chapter 23 THE NATURAL LOGARITHM 185
Chapter 24 EXPONENTIAL FUNCTIONS 195
Chapter 25 L‘HOPITAL'S RULE 208
Chapter 26 EXPONENTIAL GROWTH AND DECAY 215
Chapter 27 INVERSE TRIGONOMETRIC FUNCTIONS 220
Chapter 28 INTEGRATION BY PARTS 232
Chapter 29 TRIGONOMETRIC INTEGRANDS AND SUBSTITUTIONS 238
Chapter 30 INTEGRATION OF RATIONAL FUNCTIONS: THE METHOD OF PARTIAL FRACTIONS 245
Chapter 31 INTEGRALS FOR SURFACE AREA. WORK. CENTROIDS 253
Surface Area of a Solid of Revolution I Work I Centro'od of a Planar Region I
Chapter 32 IMPROPER INTEGRALS 260
Chapter 33 PLANAR VECTORS 268
Chapter 34 PARAMETRIC EQUATIONS. VECTOR FUNCTIONS. CURVILINEAR MOTION 274
Parametric Equations of Plane Curves I Vector-Valued Functions /
Chapter 35 POLAR COORDINATES 289
Chapter 36 INFINITE SEQUENCES 305
Chapter 37 INFINITE SERIES 312
Chapter 38 POWER SERIES 326
Chapter 39 TAYLOR AND MACLAURIN SERIES 340
Chapter 40 VECTORS IN SPACE. LINES AND PLANES 347
Chapter 41 FUNCTIONS OF SEVERAL VARIABLES 361
Multivariate Functions and Their Graphs I Cylindrical and Spherical Coordinates I
Chapter 42 PARTIAL DERIVATIVES 376
Chapter 43 DIRECTIONAL DERIVATIVES AND THE GRADIENT. EXTREME VALUES 392
Chapter 44 MULTIPLE INTEGRALS AND THEIR APPLICATIONS 405
Chapter 45 VECTOR FUNCTIONS IN SPACE. DIVERGENCE AND CURL.
LINE INTEGRALS 425
Chapter 46 DIFFERENTIAL EQUATIONS 431
INDEX 443