Schaum's Outline of Theory and Problems of Beginning Calculus

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Chapter 20Most quantities encountered in science or in everyday life vary with time. If two such quantities arerelated by an equation, and if we know the rate at which one of them changes, then, by differentiatingthe equation with respect to time, we can find the rate at which the other quantity changes.EXAMPLES(a) A 6-foot man is running away from the base of a streetlight that is 15 feet high (see Fig. 20-1). If he moves atthe rate of 18 feet per second, how fast is the length of his shadow changing?Let x be the distance of the man from the base A of the streetlight, and let y be the length of the man'sshadow.GEOMETRY Two triangles,Xare similar if their angles are equal in pairs: 3c A = %X, 3c B = % Y, % C = 3cZ. (For this condition to hold,it suffices that two angles of the one triangle be equal to two angles of the other.) Similar triangles havecorresponding sides in fixed ratio :147
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To the memory of my father, Joseph,
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6.2 Symmetry about a Point 42Chapte
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Chapter 18Rectilinear Motion and In
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Chapter 32Applications of Integrati
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2 COORDINATE SYSTEMS ON A LINE[CHAP
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~ ~ ~4 COORDINATE SYSTEMS ON A LINE
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CHAP. 11COORDINATE SYSTEMS ON A LIN
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CHAP. 23COORDINATE SYSTEMS IN A PLA
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CHAP. 21 COORDINATE SYSTEMS IN A PL
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CHAP. 2) COORDINATE SYSTEMS IN A PL
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CHAP. 31GRAPHS OF EQUATIONS15T0 0-1
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CHAP. 3) GRAPHS OF EQUATIONS 17on c
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CHAP. 31 GRAPHS OF EQUATIONS 193.5
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CHAP. 31 GRAPHS OF EQUATIONS 21x2 y
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CHAP. 31 GRAPHS OF EQUATIONS 233.16
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CHAP. 41 STRAIGHT LINES 25EXAMPLE I
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CHAP. 41STRAIGHT LINES274Ym =O m =O
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CHAP. 41AYSTRAIGHT LINESt’29Fig.
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CHAP. 41 STRAIGHT LINES 31Represent
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CHAP. 41 STRAIGHT LINES 33y-interce
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CHAP. 41STRAIGHT LINES35DAY+ Y 4YCD
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CHAP. 51 INTERSECTIONS OF GRAPHS 37
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CHAP. 51 INTERSECTIONS OF GRAPHS 39
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Chapter 6Symmetry6.1 SYMMETRY ABOUT
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CHAP. 61 SYMMETRY 43EXAMPLES(a) The
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CHAP. 61 SYMMETRY 45To solve (I) an
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CHAP. 71FUNCTIONS AND THEIR GRAPHS4
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CHAP. 73 FUNCTIONS AND THEIR GRAPHS
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CHAP. 71FUNCTIONS AND THEIR GRAPHS
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CHAP. 71 FUNCTIONS AND THEIR GRAPHS
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CHAP. 71FUNCTIONS AND THEIR GRAPHS
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CHAP. 71FUNCTIONS AND THEIR GRAPHSt
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Chapter 8Limits8.1 INTRODUCTIONTo a
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CHAP. 81 LIMITS 61EXAMPLElim ,/- =
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CHAP. 83 LIMITS 63(b) f(x + h) = 4(
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CHAP. 8) LIMITS 65Supplementary Pro
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Chapter 9Special Limits9.1 ONE-SIDE
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CHAP. 91 SPECIAL LIMITS 69to indica
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CHAP. 93 SPECIAL LIMITS 71EXAMPLESl
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CHAP. 91 SPECIAL LIMITS 73EXAMPLE D
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CHAP. 91 SPECIAL LIMITS 75lim f(x)
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CHAP. 91 SPECIAL LIMITS 77(b) Assum
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~ ~~ ~~~~~~~~~~~~~~~~~~~~CHAP. 101
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CHAP. 101 CONTINUITY 81Solved Probl
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CHAP. 101 CONTINUITY a3(a) There ar
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CHAP. 101 CONTINUITY 8510.12For eac
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h,CHAP. 11) THE SLOPE OF A TANGENT
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CHAP. 113THE SLOPE OF A TANGENT LIN
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CHAP. 113 THE SLOPE OF A TANGENT LI
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CHAP. 121 THE DERIVATIVE 93CoroUary
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h,CHAP. 121 THE DERIVATIVE 95Solved
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CHAP. 121 THE DERIVATIVE 9712.8(a)
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Chapter 13More on the Derivative13.
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h,~ ~~CHAP. 131 MORE ON THE DERIVAT
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CHAP. 13) MORE ON THE DERIVATIVE 10
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CHAP. 14) MAXIMUM AND MINIMUM PROBL
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~CHAP. 14)MAXIMUM AND MINIMUM PROBL
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CHAP. 141 MAXIMUM AND MINIMUM PROBL
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CHAP. 141 MAXIMUM AND MINIMUM PROBL
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~ ~ ~~CHAP. 141 MAXIMUM AND MINIMUM
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CHAP. 141MAXIMUM AND MINIMUM PROBLE
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CHAP. 151 THE CHAIN RULE 117(6) Let
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CHAP. 151 THE CHAIN RULE 119EXAMPLE
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Page 278: CHAP. 161IMPLICIT DIFFERENTIATION12
Page 282: Chapter 17The Mean-Value Theorem an
Page 286: CHAP. 17) THE MEAN-VALUE THEOREM AN
Page 290: CHAP. 173 THE MEAN-VALUE THEOREM AN
Page 294: h,CHAP. 171 THE MEAN-VALUE THEOREM
Page 298: CHAP. 181RECTILINEAR MOTION AND INS
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Page 310: Chapter 19Instantaneous Rate of Cha
Page 314: CHAP. 191INSTANTANEOUS RATE OF CHAN
Page 320: 148 RELATED RATES [CHAP. 20In Fig.
Page 324: 150 RELATED RATES [CHAP. 20- XFig.
Page 328: 152 RELATED RATES[CHAP. 20and, by (
Page 332: 154 RELATED RATES [CHAP. 2020.21 A
Page 336: 156 APPROXIMATION BY DIFFERENTIALS;
Page 340: 158 APPROXIMATION BY DIFFERENTIALS;
Page 344: 1 60APPROXIMATION BY DIFFERENTIALS;
Page 348: 1 62 HIGHER-ORDER DERIVATIVES [CHAP
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Page 356: 166 HIGHER-ORDER DERIVATIVES [CHAP.
Page 360: 168 THE SECOND DERIVATIVE AND GRAPH
Page 364: 170 THE SECOND DERIVATIVE AND GRAPH
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172 THE SECOND DERIVATIVE AND GRAPH
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23.7 If, for all x,f’(x) > 0 andf
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180 MORE MAXIMUM AND MINIMUM PROBLE
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186 ANGLE MEASURE [CHAP. 25and so o
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188 ANGLE MEASURE [CHAP. 25Solved P
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Chapter 2626.1 GENERAL DEFINITIONSi
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192 SINE AND COSINE FUNCTIONS [CHAP
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~~~ ~196 SINE AND COSINE FUNCTIONS
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Chapter 27Graphs and Derivatives of
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204 GRAPHS AND DERIVATIVES OF SINE
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212GRAPHS AND DERIVATIVES OF SINE A
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Chapter 28The Tangent andOther Trig
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216 THE TANGENT AND OTHER TRIGONOME
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222 ANTIDERIVATIVES [CHAP. 29EXAMPL
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224 ANTIDERIVATIVES [CHAP. 29(ii) F
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226 ANTIDERIVATIVES [CHAP. 2929.5 A
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228 ANTIDERIVATIVES [CHAP. 2929.13
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230 THE DEFINITE INTEGRAL [CHAP. 30
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232 THE DEFINITE INTEGRAL [CHAP. 30
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234 THE DEFINlTE INTEGRAL (CHAP.[I)
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’)236 THE DEFINITE INTEGRAL [CHAP
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Chapter 31The Fundamental Theorem o
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240 THE FUNDAMENTAL THEOREM OF CALC
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250 APPLICATlONS OF INTEGRATION I:
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252 APPLICATIONS OF INTEGRATION I:
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258 APPLlCATlONS OF INTEGRATION 11:
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260 APPLICATIONS OF INTEGRATION 11:
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266 APPLICATIONS OF INTEGRATION I1
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Chapter 3434.1 DEFlMTlONWe already
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270 THE NATURAL LOGARITHM [CHAP. 34
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272 THE NATURAL LOGARITHM [CHAP. 34
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(b)27434.14THE NATURAL LOGARITHM11(
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276 EXPONENTIAL FUNCTIONS [CHAP. 35
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278EXPONENTIAL FUNCTIONS[CHAP. 3535
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Chapter 36L’HGpital’s Rule ; Ex
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286 L'HOPITAL'S RULE; EXPONENTIAL G
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288 L'H~PITAL'S RULE; EXPONENTIAL G
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290 L'HQPITAL'S RULE; EXPONENTIAL G
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~~~~~~~~ ~ ~~~ ~ ~ ~ ~ ~ ~ ~Chapter
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294 INVERSE TRIGONOMETRIC FUNCTIONS
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above304 INVERSE TRIGONOMETRIC FUNC
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~ du=dx306 INTEGRATION BY PARTS [CH
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308 INTEGRATION BY PARTS[CHAP. 3838
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3 10INTEGRATION BY PARTS[CHAP. 38Su
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312 TRIGONOMETRIC INTEGRANDS AND TR
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Chapter 40Integration of Rational F
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322 THE METHOD OF PARTIAL FRACTIONS
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Appendix BBasic Integration Formula
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0"1"2"3"4"5"6"7"8"9"10"11"12"13"14"
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Appendix F-X0.000.050.100.150.200.2
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336 ANSWERS. TO SUPPLEMENTARY PROBL
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338ANSWERS TO SUPPLEMENTARY PROBLEM
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340 ANSWERS TO SUPPLEMENTARY PROBLE
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R-v QdA 1d 1
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364+I)ANSWERS TO SUPPLEM ENTARY PRO
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Collinear points, 30Common logarith
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Infinite limits, 68Inflection point
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RRadian, 185Radicals, 118Range, 47R
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Schaum's Outline of Theory and Problems of Beginning Calculus

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