,
,
, 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 APPROXIMATION 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
iii
,
, 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 APPROXIMATION 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
iii
