CALCULUS

By O. HILAO

CONTENTS ANALYTIC GEOMETRY LINES DISTANCE BETWEEN TWO POINTS; CIRCLES FUNCTIONS SHIFTS AND DILATIONS INSTANTANEOUS RATE OF CHANGE: THE DERIVATIVE THE SLOPE OF A FUNCTION AN EXAMPLE LIMITS THE DERIVATIVE FUNCTION ADJECTIVES FOR FUNCTIONS RULES FOR FINDING DERIVATIVES THE POWER RULE LINEARITY OF THE DERIVATIVE THE PRODUCT RULE THE QUOTIENT RULE THE CHAIN RULE TRANSCENDENTAL FUNCTIONS TRIGONOMETRIC FUNCTIONS THE DERIVATIVE OF SIN X A HARD LIMIT THE DERIVATIVE OF SIN X, CONTINUED DERIVATIVES OF THE TRIGONOMETRIC FUNCTIONS EXPONENTIAL AND LOGARITHMIC FUNCTIONS DERIVATIVES OF THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS LIMITS REVISITED IMPLICIT DI?ERENTIATION INVERSE TRIGONOMETRIC FUNCTIONS CURVE SKETCHING MAXIMA AND MINIMA THE ?RST DERIVATIVE TEST THE SECOND DERIVATIVE TEST CONCAVITY AND IN?ECTION POINTS ASYMPTOTES AND OTHER THINGS TO LOOK FOR APPLICATIONS OF THE DERIVATIVE OPTIMIZATION RELATED RATES NEWTON’S METHOD LINEAR APPROXIMATIONS THE MEAN VALUE THEOREM INTEGRATION TWO EXAMPLES THE FUNDAMENTAL THEOREM OF CALCULUS SOME PROPERTIES OF INTEGRALS TECHNIQUES OF INTEGRATION SUBSTITUTION POWERS OF SINE AND COSINE TRIGONOMETRIC SUBSTITUTIONS INTEGRATION BY PARTS RATIONAL FUNCTIONS ADDITIONAL EXERCISES APPLICATIONS OF INTEGRATION AREA BETWEEN CURVES DISTANCE, VELOCITY, ACCELERATION VOLUME AVERAGE VALUE OF A FUNCTION WORK CENTER OF MASS KINETIC ENERGY; IMPROPER INTEGRALS PROBABILITY ARC LENGTH SURFACE AREA DI?ERENTIAL EQUATIONS SEQUENCES AND SERIES SEQUENCES SERIES THE INTEGRAL TEST ALTERNATING SERIES COMPARISON TESTS ABSOLUTE CONVERGENCE THE RATIO AND ROOT TESTS POWER SERIES CALCULUS WITH POWER SERIES TAYLOR SERIES TAYLOR’S THEOREM A INTRODUCTION TO MAPLE GETTING STARTED ALGEBRA A 2 1 NUMBERS A 2 2 VARIABLES AND EXPRESSIONS A 2 3 EVALUATION AND SUBSTITUTION A 2 4 SOLVING EQUATIONS PLOTTING CALCULUS A 4 1 LIMITS A 4 2 DI?ERENTIATION A 4 3 IMPLICIT DI?ERENTIATION A 4 4 INTEGRATION ADDING TEXT TO A MAPLE SESSION PRINTING SAVING YOUR WORK GETTING HELP B SELECTED ANSWERS