Stewart Single Variable Calculus Early Transcendentals 7th txtbk.pdf

97909_FrontEP_FrontEP_pF2_RefPage1-2_97909_FrontEP_FrontEP_pF2_RefPage1-29/24/105:36PMPage1REFERENCEPAGE1ALGEBRAGEOMETRYArithmeticOperationsGeometricFormulasacadϩbcACVa͑bϩc͒෇abϩacϩ෇Formulasforarea,circumference,andvolume:bdbdTriangleCircleSectorofCirclea෇1෇␲2෇12␪ϩA2bhArA2rac෇aϩcb෇aϫd෇ad෇1␪෇␲෇␪͑␪͒bbbcbcbc2absinC2rsrinradiansdaExponentsandRadicalshrsm¨rmnmϩnxmϪnCuthereandkeepforreference෇෇¨xxxnxbxr1͑xm͒n෇xmnxϪn෇xnxnxnSphereCylinderCone͑xy͒n෇xnynͩͪ෇yyn෇4␲3෇␲2෇1␲2V3rVrhV3rhx1͞n෇snxxm͞n෇snxm෇(snx)mA෇4␲r2A෇␲rsr2ϩh2xsnxsnxy෇snxsnyͱn෇rysnyrhhFactoringSpecialPolynomialsrx2Ϫy2෇͑xϩy͒͑xϪy͒x3ϩy3෇͑xϩy͒͑x2Ϫxyϩy2͒x3Ϫy3෇͑xϪy͒͑x2ϩxyϩy2͒DistanceandMidpointFormulasBinomialTheoremDistancebetweenP1͑x1,y1͒andP2͑x2,y2͒:͑xϩy͒2෇x2ϩ2xyϩy2͑xϪy͒2෇x2Ϫ2xyϩy2෇s͑Ϫ͒2ϩ͑Ϫ͒2͑xϩy͒3෇x3ϩ3x2yϩ3xy2ϩy3dx2x1y2y1͑xϪy͒3෇x3Ϫ3x2yϩ3xy2Ϫy3ϩϩ͑Ϫ͒x1x2y1y2Ϫnn1ϪMidpointofPP:ͩ,ͪ͑xϩy͒n෇xnϩnxn1yϩxn2y212222nϩиииϩͩͪxnϪkykϩиииϩnxynϪ1ϩynkLinesnn͑nϪ1͒иии͑nϪkϩ1͒whereͩͪ෇hroughP͑x,y͒andP͑x,y͒:k1ؒ2ؒ3ؒиииؒk111222yϪyQuadraticFormulam෇21x2Ϫx1ϪbϮsb2Ϫ4acIfax2ϩbxϩc෇0,thenx෇.2aPoint-hroughP1͑x1,y1͒withslopem:InequalitiesandAbsoluteValueyϪy1෇m͑xϪx1͒IfaϽbandbϽc,-interceptequationoflinewithslopemandy-interceptb:IfaϽb,,෇mxϩbIfaϽbandcϽ0,,thenCirclesԽxԽ෇ameansx෇aorx෇ϪaEquationofthecirclewithcenter͑h,k͒andradiusr:ԽxԽϽameansϪaϽxϽaԽxԽϾameansxϾaorxϽϪa͑xϪh͒2ϩ͑yϪk͒2෇r297909_FrontEP_FrontEP_pF2_RefPage1-2_97909_FrontEP_FrontEP_pF2_RefPage1-29/24/105:36PMPage2REFERENCEPAGE2TRIGONOMETRYAngleMeasurementFundamentalIdentities␲radians෇180Њ11scsc␪෇sec␪෇rsin␪cos␪␲180ЊЊ෇෇¨1rad1rad␲␪␪180␪෇sin␪෇cosrtan␪cot␪s෇r␪cossin͑␪͒1inradianscot␪෇sin2␪ϩcos2␪෇1tan␪RightAngleTrigonometry1ϩtan2␪෇sec2␪1ϩcot2␪෇csc2␪opphypsin␪෇csc␪෇͑Ϫ␪͒෇Ϫ␪͑Ϫ␪͒෇␪hypopphypsinsincoscosoppadjhyp␲cos␪෇sec␪෇¨tan͑Ϫ␪͒෇Ϫtan␪sinͩϪ␪ͪ෇cos␪hypadjadj2oppadjtan␪෇cot␪෇␲␲adjoppcosͩϪ␪ͪ෇sin␪tanͩϪ␪ͪ෇cot␪22TrigonometricFunctionsTheLawofSinesByrysin␪෇csc␪෇rysinA෇sinB෇sinCaabcxr(x, y)cos␪෇sec␪෇rCrxcyx¨TheLawofCosinestan␪෇cot␪෇xxyba2෇osAGraphsofTrigonometricFu