Introductory Mathematical Analysis By Haeussler Paul And Wood Pdf

Unformatted text preview: HAEUSSLER JR. PAUL WOOD F O R B U S IN E S S , E C O N O M IC S , A N D THE LIF E A ND S OCIA L S C IE NC E S INTRODUCTORY MATHEMATICAL ANALYSIS About the Cover The Royal Ontario Museum (ROM) in Toronto, Canada, opened in March 1914. The ROM has undergone several overhauls, the most dramatic being the addition of Daniel Libeskind's Lee-Chin Crystal, finished in June of 2007. The soaring glass and metal structure leads a visitor from the chaos of the street to the more serene atmosphere FO U RT E EN T H E DI T I O N of the museum. Like many modern buildings, the Crystal embodies application of many areas of mathematics in many ways. Readers of the linear programming chapter (7) of this book may find it useful to glance at the cover while contemplating routes, via edges, between the vertices of similar structures. ISBN 978-0-13-414110-7 9 780134 141107 90000 INTRODUCTORY MATHEMATICAL ANALYSIS ERNEST F. HAEUSSLER JR. RICHARD S. PAUL RICHARD J. WOOD FOR BUSINESS, ECONOMICS, AND THE LIFE AND SOCIAL SCIENCES FOURTEENTH EDITION This page intentionally left blank 561590_MILL_MICRO_FM_ppi-xxvi.indd 2 24/11/14 5:26 PM +DHXVVOHU &95B+$(8BB6(B,)& 1RYHPEHU $/*(%5$ ([SRQHQWV $OJHEUDLF 5XOHV IRU 5HDO QXPEHUV D D DCEDECD DE D ED D C .E C F/ D .D C E/ C F D.EF/ D .DE/F D.E C F/ D DE C DF D.E ! F/ D DE ! DF .D C E/F D DF C EF .D ! E/F D DF ! EF DCDD D"D D"DD D C .!D/ D !.!D/ D D .!/D D !D D ! E D D C .!E/ D! ! .!E/ " DDCE D D D D DD" E E .D ¤ / DQ DP DQ D DPCQ .DP /Q D DPQ .DE/Q D DQ EQ # D $Q DQ D Q E E P D D DP!Q DQ D!Q D 6SHFLDO 3URGXFWV [.\ C ]/ D [\ C .[ C D/.[ C E/ D [ C .D C E/[ C DE .[ C D/ D [ C D[ C D .[ ! D/ D [ ! D[ C D .[ C D/.[ ! D/ D [ ! D .[ C D/ D [ C D[ C D [ C D .[ ! D/ D [ ! D[ C D [ ! D .!D/E D !.DE/ D D.!E/ .!D/.!E/ D DE 4XDGUDWLF )RUPXOD !D D D !E E !D D D D! D E E !E D E DCE C D F F F D E D!E ! D F F F D F DF " D E G EG D=E DG D F=G EF D DF D .F ¤ / E EF ,I D[ C E[ C F D ZKHUH D ¤ WKHQ p !E ˙ E ! DF [D D ,QHTXDOLWLHV ,I D < E WKHQ D C F < E C F ,I D < E DQG F > WKHQ DF < EF ,I D < E DQG F > WKHQ D.!F/ > E.!F/ 6XPPDWLRQ )RUPXODV Q P LDP Q P FDL D F Q P LDP .DL C EL / D LDP Q P LDP S! P LDP DL D DL C SCQ!P P LDS Q P LDS 6SHFLDO 6XPV DL Q P LDP DL C DLCP!S DL D Q P LDP DL Q P LDP EL Q P DQ LD Q P L D Q.QC/.QC/ L D Q .QC/ LD Q P LD Q P LD LD Q.QC/ 5DGLFDOV p Q D D D=Q p p Q . D/Q D D; Q DQ D D .D > / p p P Q DP D . Q D/ D DP=Q p p p Q Q Q D E rDE D p Q D D Q Dp Q E Ep p p P Q D D PQ D )DFWRULQJ )RUPXODV DE C DF D D.E C F/ D ! E D .D C E/.D ! E/ D C DE C E D .D C E/ D ! DE C E D .D ! E/ D C E D .D C E/.D ! DE C E / D ! E D .D ! E/.D C DE C E / 6WUDLJKW /LQHV \ ! \ [ ! [ \ ! \ D P.[ ! [ / \ D P[ C E [ D FRQVWDQW \ D FRQVWDQW PD VORSH IRUPXOD SRLQWVORSH IRUP VORSHLQWHUFHSW IRUP YHUWLFDO OLQH KRUL]RQWDO OLQH $EVROXWH 9DOXH jDEj D jDj " jEj ˇDˇ jDj ˇ ˇ ˇ ˇD E jEj jD ! Ej D jE ! Dj !jDj # D # jDj jD C Ej # jDj C jEj WULDQJOH LQHTXDOLW\ /RJDULWKPV ORJE [ D \ LI DQG RQO\ LI [ D E\ ORJE .PQ/ D ORJE P C ORJE Q P ORJE D ORJE P ! ORJE Q Q ORJE PU D U ORJE P ORJE D ORJE E D ORJE EU D U EORJE S D S .S > / ORJD P ORJE P D ORJD E +DHXVVOHU &95B+$(8BB6(B,)& 1RYHPEHU ),1,7( 0$7+(0$7,&6 &RPSRXQG ,QWHUHVW )RUPXODV %XVLQHVV 5HODWLRQV ,QWHUHVW D SULQFLSDO UDWH WLPH 7RWDO FRVW D YDULDEOH FRVW C ı[HG FRVW WRWDO FRVW $YHUDJH FRVW SHU XQLW D TXDQWLW\ 7RWDO UHYHQXH D SULFH SHU XQLW QXPEHU RI XQLWV VROG 3URıW D WRWDO UHYHQXH ! WRWDO FRVW 6 D 3. C U/Q 3 D 6. C U/!Q # U $Q UH D C ! Q 6 D 3HUW 3 D 6H!UW UH D HU ! 2UGLQDU\ $QQXLW\ )RUPXODV ! . C U/!Q $D5 D 5DQ U U Q . C U/ ! 6D5 D 5VQ U U 0DWUL[ 0XOWLSOLFDWLRQ SUHVHQW YDOXH IXWXUH YDOXH .$%/LN D Q X MD $LM %MN D $L %N C $L %N C " " " C $LQ EQN .$%/7 D %7 $7 &RXQWLQJ $! $ D , D $$! .$%/! D %! $! QŠ .Q ! U/Š QŠ Q &U D UŠ.Q ! U/Š Q Q & C Q & C " " " C Q &Q! C Q &Q D Q 3U Q & D 3UREDELOLW\ 3.(/ D D D Q &Q QC &UC 3.(j)/ D D Q &U C Q &UC .( \ )/ .)/ 3.( [ )/ D 3.(/ C 3.)/ ! 3.( \ )/ 3.(0 / D ! 3.(/ 3.( \ )/ D 3.(/3.)j(/ D 3.)/3.(j)/ 3URSHUWLHV RI (YHQWV )RU ( DQG ) HYHQWV IRU DQ H[SHULPHQW ZLWK VDPSOH VSDFH 6 ([(D( ($D( .(0 /0 D ( ( [ (0 D 6 ( \ (0 D ; ([6D6 (\6D( ([;D( (\;D; ([)D)[( ($D)\( .( [ )/0 D (0 \ )0 .( \ )/0 D (0 [ )0 ( [ .) [ */ D .( [ )/ [ * ( \ .) \ */ D .( \ )/ \ * ( \ .) [ */ D .( \ )/ [ .( \ */ ( [ .) \ */ D .( [ )/ \ .( [ */ .(/ .6/ )RU ; D GLVFUHWH UDQGRP YDULDEOH ZLWK GLVWULEXWLRQ I X [ I.[/ D " D ".;/ D (.;/ D X [I.[/ X 9DU.;/ D (..; ! "/ / D .[ ! "/ I.[/ [ p # D #.;/ D 9DU.;/ [ %LQRPLDO GLVWULEXWLRQ I.[/ D 3.; D [/ D Q &[ S[ TQ![ " D QS p # D QST +DHXVVOHU &95B+$(8BB6(B,)& 1RYHPEHU &$/&8/86 *UDSKV RI (OHPHQWDU\ )XQFWLRQV y y 2 y 4 f(x) = 1 4 2 -2 1 -1 2 2 -2 -4 2 -2 x -4 2 -2 -2 -2 -2 -4 -4 -4 y f(x) = x 4 x -4 4 2 2 2 -2 2 x3 f (x) = 4 2 -2 4 -4 2 -2 4 x -4 2 -2 -2 -2 -2 -2 -4 -4 -4 -4 y 4 2 y f(x) = 1x 2 -2 4 y f(x) = 12 x -4 2 -2 4 f(x) = ex 4 f(x) = lnx x -4 2 2 -2 4 x -4 2 -2 -2 -2 -2 -4 -4 -4 -4 'LĳHUHQWLDWLRQ )RUPXODV G GX .OQ X/ D G[ X G[ G .FI.[// D FI0 .[/ G[ G X GX .H / D HX G[ G[ G . I.[/ ˙ J.[// D I0 .[/ ˙ J0 .[/ G[ G GX .ORJE X/ D " G[ .OQ E/X G[ G . I.[/J.[// D I.[/J0 .[/ C J.[/ I0 .[/ G[ SURGXFW UXOH ! " G I.[/ J.[/ I0 .[/ ! I.[/J0 .[/ D G[ J.[/ .J.[// TXRWLHQW UXOH G X GX .E / D EX .OQ E/ G[ G[ G\ G\ GX D " G[ GX G[ G\ D G[ G[ G\ FKDLQ UXOH G ! . I .[// D 0 ! G[ I . I .[// x S T S GT $D " D GS T GS GT G I.[ C K/ ! I.[/ I.]/ ! I.[/ . I.[// D OLP D OLP![ K! G[ K![ G D .[ / D D[D! G[ 4 (ODVWLFLW\ IRU 'HPDQG T D T.S/ 'HıQLWLRQ RI 'HULYDWLYH RI I.[/ G D GX .X / D DXD! G[ G[ x 4 -2 G .F/ D G[ 4 y 2 x f(x) = x 2 x x 4 y y f(x) = 3 x 4 2 I0 .[/ D 4 -2 4 -4 x f(x) = x3 2 -1 y -4 4 4 f(x) = x2 2 f(x) = x x -4 y ,QWHJUDWLRQ )RUPXODV Z Z :H DVVXPH WKDW X LVZD GLĳHUHQWLDEOH IXQFWLRQ Z RI [ N G[ D N[ C & Z . I.[/ ˙ J.[// G[ D I.[/ G[ ˙ [DC XDC C &; D ¤ ! XD GX D C &; D ¤ DC DC Z Z H[ G[ D H[ C & HX GX D HX C & Z Z Z NI.[/ G[ D N I.[/ G[ GX D OQ jXj C &; X ¤ X [D G[ D &RQVXPHUVŖ 6XUSOXV IRU 'HPDQG S D I.T/ Z T &6 D Œ I.T/ ! S % GT 3URGXFHUVŖ 6XUSOXV IRU 6XSSO\ S D J.T/ 36 D R T Œ S ! J.T/% GT Z J.[/ G[ +DHXVVOHU $B+$(8BB6(B)0 1RYHPEHU INTRODUCTORY MATHEMATICAL ANALYSIS ERNEST F. HAEUSSLER JR. The Pennsylvania State University RICHARD S. PAUL The Pennsylvania State University RICHARD J. WOOD Dalhousie University FOR BUSINESS, ECONOMICS, AND THE LIFE AND SOCIAL SCIENCES FOURTEENTH EDITION +DHXVVOHU $B+$(8BB6(B)0 1RYHPEHU 3ǀƽƲǃƱǂƷƽƼ 6ƳǀǄƷƱƳǁ &HQYHRŪ 3XEOLVKHU 6HUYLFHV 3ƳǀƻƷǁǁƷƽƼǁ 3ǀƽƸƳƱǂ 0ƯƼƯƵƳǀ &DWKHULQH %HOYHGHUH -RDQQH 7DQJ 3ƶƽǂƽ 3ƳǀƻƷǁǁƷƽƼǁ 5ƳǁƳƯǀƱƶ ,QWHJUD 3XEOLVKLQJ 6HUYLFHV 7Ƴǆǂ 3ƳǀƻƷǁǁƷƽƼǁ 5ƳǁƳƯǀƱƶ ,QWHJUD 3XEOLVKLQJ 6HUYLFHV &ƽǄƳǀ 'ƳǁƷƵƼƳǀ $QWKRQ\ /HXQJ &ƽǄƳǀ ,ƻƯƵƳ 'D\2ZO 6KXWWHUVWRFNFRP 9ƷƱƳ3ǀƳǁƷƲƳƼǂ &ǀƽǁǁ 0ƳƲƷƯ ƯƼƲ 3ǃưƺƷǁƶƷƼƵ 6ƳǀǄƷƱƳǁ *DU\ %HQQHWW 9ƷƱƳ 3ǀƳǁƷƲƳƼǂ (ƲƷǂƽǀƷƯƺ $QQH :LOOLDPV $ƱƿǃƷǁƷǂƷƽƼǁ (ƲƷǂƽǀ -HQQLIHU 6XWWRQ 0ƯǀƹƳǂƷƼƵ 0ƯƼƯƵƳǀ .\ 3UXHVVH &ƽƼǂƳƼǂ 0ƯƼƯƵƳǀ (PLO\ 'LOO 3ǀƽƸƳƱǂ 0ƯƼƯƵƳǀ 3LSSD .HQQDUG &ƽƼǂƳƼǂ 'ƳǄƳƺƽƾƳǀ 7DPDUD &DSDU 0ƳƲƷƯ 'ƳǄƳƺƽƾƳǀ .HOOL &DGHW 3HDUVRQ &DQDGD ,QF 3ULQFH $QGUHZ 3ODFH 1RUWK <RUN 2QWDULR 0& + &RS\ULJKW ũ 3HDUVRQ &DQDGD ,QF $OO ULJKWV UHVHUYHG 3ULQWHG LQ WKH 8QLWHG 6WDWHV RI $PHULFD 7KLV SXEOLFDWLRQ LV SURWHFWHG E\ FRS\ULJKW DQG SHUPLVVLRQ VKRXOG EH REWDLQHG IURP WKH SXEOLVKHU SULRU WR DQ\ SURKLELWHG UHSURGXFWLRQ VWRUDJH LQ D UHWULHYDO V\VWHP RU WUDQVPLVVLRQ LQ DQ\ IRUP RU E\ DQ\ PHDQV HOHFWURQLF PHFKDQLFDO SKRWRFRS\LQJ UHFRUGLQJ RU RWKHUZLVH )RU LQIRUPDWLRQ UHJDUGLQJ SHUPLVVLRQV UHTXHVW IRUPV DQG WKH DSSURSULDWH FRQWDFWV SOHDVH FRQWDFW 3HDUVRQ &DQDGDŖV 5LJKWV DQG 3HUPLVVLRQV 'HSDUWPHQW E\ YLVLWLQJ ZZZ SHDUVRQFDQDGDFDFRQWDFWLQIRUPDWLRQSHUPLVVLRQVUHTXHVWV $WWULEXWLRQV RI WKLUGSDUW\ FRQWHQW DSSHDU RQ WKH DSSURSULDWH SDJH ZLWKLQ WKH WH[W 3($5621 LV DQ H[FOXVLYH WUDGHPDUN RZQHG E\ 3HDUVRQ &DQDGD ,QF RU LWV DĴ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ĴOLDWHV DXWKRUV OLFHQVHHV RU GLVWULEXWRUV /LEUDU\ DQG $UFKLYHV &DQDGD &DWDORJXLQJ LQ 3XEOLFDWLRQ +DHXVVOHU (UQHVW ) DXWKRU ,QWURGXFWRU\ PDWKHPDWLFDO DQDO\VLV IRU EXVLQHVV HFRQRPLFV DQG WKH OLIH DQG VRFLDO VFLHQFHV (UQHVW ) +DHXVVOHU -U 7KH 3HQQV\OYDQLD 6WDWH 8QLYHUVLW\ 5LFKDUG 6 3DXO 7KH 3HQQV\OYDQLD 6WDWH 8QLYHUVLW\ 5LFKDUG - :RRG 'DOKRXVLH 8QLYHUVLW\Š)RXUWHHQWK HGLWLRQ ,QFOXGHV ELEOLRJUDSKLFDO UHIHUHQFHV DQG LQGH[ ,6%1 KDUGFRYHU 0DWKHPDWLFDO DQDO\VLV (FRQRPLFV 0DWKHPDWLFDO %XVLQHVV PDWKHPDWLFV , 3DXO 5LFKDUG 6 DXWKRU ,, :RRG 5LFKDUG -DPHV DXWKRU ,,, 7LWOH 4$+ & +DHXVVOHU $B+$(8BB6(B)0 1RYHPEHU 'PS #SPOXFO This page intentionally left blank 561590_MILL_MICRO_FM_ppi-xxvi.indd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Ĳ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ŖV ,QSXW2XWSXW $QDO\VLV &KDSWHU 5HYLHZ -JOFBS 1SPHSBNNJOH /LQHDU ,QHTXDOLWLHV LQ 7ZR 9DULDEOHV /LQHDU 3URJUDPPLQJ 7KH 6LPSOH[ 0HWKRG $UWLıFLDO 9DULDEOHV 0LQLPL]DWLRQ 7KH 'XDO &KDSWHU 5HYLHZ *OUSPEVDUJPO UP 1SPCBCJMJUZ BOE 4UBUJTUJDT %DVLF &RXQWLQJ 3ULQFLSOH DQG 3HUPXWDWLRQV &RPELQDWLRQV DQG 2WKHU &RXQWLQJ 3ULQFLSOHV 6DPSOH 6SDFHV DQG (YHQWV 3UREDELOLW\ &RQGLWLRQDO 3UREDELOLW\ DQG 6WRFKDVWLF 3URFHVVHV ,QGHSHQGHQW (YHQWV %D\HVŖ )RUPXOD &KDSWHU 5HYLHZ "EEJUJPOBM 5PQJDT JO 1SPCBCJMJUZ 'LVFUHWH 5DQGRP 9DULDEOHV DQG ([SHFWHG 9DOXH 7KH %LQRPLDO 'LVWULEXWLRQ 0DUNRY &KDLQV &KDSWHU 5HYLHZ +DHXVVOHU $B+$(8BB6(B)0 1RYHPEHU &RQWHQWV 1"35 *** $)"15&3 $)"15&3 $)"15&3 $)"15&3 $)"15&3 $"-$6-64 -JNJUT BOE $POUJOVJUZ /LPLWV /LPLWV &RQWLQXHG &RQWLQXLW\ &RQWLQXLW\ $SSOLHG WR ,QHTXDOLWLHV &KDSWHU 5HYLHZ %JøFSFOUJBUJPO 7KH 'HULYDWLYH 5XOHV IRU 'LĳHUHQWLDWLRQ 7KH 'HULYDWLYH DV D 5DWH RI &KDQJH 7KH 3URGXFW 5XOH DQG WKH 4XRWLHQW 5XOH 7KH &KDLQ 5XOH &KDSWHU 5HYLHZ "EEJUJPOBM %JøFSFOUJBUJPO 5PQJDT 'HULYDWLYHV RI /RJDULWKPLF )XQFWLRQV 'HULYDWLYHV RI ([SRQHQWLDO )XQFWLRQV (ODVWLFLW\ RI 'HPDQG ,PSOLFLW 'LĳHUHQWLDWLRQ /RJDULWKPLF 'LĳHUHQWLDWLRQ 1HZWRQŖV 0HWKRG +LJKHU2UGHU 'HULYDWLYHV &KDSWHU 5HYLHZ $VSWF 4LFUDIJOH 5HODWLYH ([WUHPD $EVROXWH ([WUHPD RQ D &ORVHG ,QWHUYDO &RQFDYLW\ 7KH 6HFRQG'HULYDWLYH 7HVW $V\PSWRWHV $SSOLHG 0D[LPD DQG 0LQLPD &KDSWHU 5HYLHZ *OUFHSBUJPO 'LĳHUHQWLDOV 7KH ,QGHıQLWH ,QWHJUDO ,QWHJUDWLRQ ZLWK ,QLWLDO &RQGLWLRQV 0RUH ,QWHJUDWLRQ )RUPXODV 7HFKQLTXHV RI ,QWHJUDWLRQ 7KH 'HıQLWH ,QWHJUDO 7KH )XQGDPHQWDO 7KHRUHP RI &DOFXOXV &KDSWHU 5HYLHZ YLL +DHXVVOHU YLLL $B+$(8BB6(B)0 1RYHPEHU &RQWHQWV $)"15&3 $)"15&3 $)"15&3 "QQMJDBUJPOT PG *OUFHSBUJPO ,QWHJUDWLRQ E\ 7DEOHV $SSUR[LPDWH ,QWHJUDWLRQ $UHD %HWZHHQ &XUYHV &RQVXPHUVŖ DQG 3URGXFHUVŖ 6XUSOXV $YHUDJH 9DOXH RI D )XQFWLRQ 'LĳHUHQWLDO (TXDWLRQV 0RUH $SSOLFDWLRQV RI 'Lĳ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ıHOGV DQG PDMRUV DV VXJJHVWHG E\ WKH WLWOH $V EHJXQ LQ WKH WKLUWHHQWK HGLWLRQ WKH ERRN KDV WKUHH SDUWV &ROOHJH $OJHEUD &KDSWHUV ş )LQLWH 0DWKHPDWLFV &KDSWHUV ş DQG &DOFXOXV &KDSWHUV ş 6FKRROV WKDW KDYH WZR DFDGHPLF WHUPV SHU \HDU WHQG WR JLYH %XVLQHVV VWXGHQWV D WHUP GHYRWHG WR )LQLWH 0DWKHPDWLFV DQG D WHUP GHYRWHG WR &DOFXOXV )RU WKHVH VFKRROV ZH UHF RPPHQG &KDSWHUV WKURXJK IRU WKH ıUVW FRXUVH VWDUWLQJ ZKHUHYHU WKH SUHSDUDWLRQ RI WKH VWXGHQWV DOORZV DQG &KDSWHUV WKURXJK IRU WKH VHFRQG LQFOXGLQJ DV PXFK DV WKH VWX GHQWVŖ EDFNJURXQG DOORZV DQG WKHLU QHHGV GLFWDWH )RU VFKRROV ZLWK WKUHH TXDUWHU RU WKUHH VHPHVWHU FRXUVHV SHU \HDU WKHUH DUH D QXPEHU RI SRVVLEOH XVHV IRU WKLV ERRN ,I WKHLU SURJUDP DOORZV WKUHH TXDUWHUV RI 0DWKHPDWLFV ZHOO SUHSDUHG %XVLQHVV VWXGHQWV FDQ VWDUW D ıUVW FRXUVH RQ )LQLWH 0DWKHPDWLFV ZLWK &KDSWHU DQG SURFHHG WKURXJK WRSLFV RI LQWHUHVW XS WR DQG LQFOXGLQJ &KDSWHU ,Q WKLV VFHQDULR D VHFRQG FRXUVH RQ 'LĳHUHQWLDO &DOFXOXV FRXOG VWDUW ZLWK &KDSWHU RQ /LPLWV DQG &RQWLQX LW\ IROORZHG E\ WKH WKUHH ŗGLĳHUHQWLDWLRQ FKDSWHUVŘ WKURXJK LQFOXVLYH +HUH 6HFWLRQ RQ 1HZWRQŖV 0HWKRG FDQ EH RPLWWHG ZLWKRXW ORVV RI FRQWLQXLW\ ZKLOH VRPH LQVWUXFWRUV PD\ SUHIHU WR UHYLHZ &KDSWHU RQ ([SRQHQWLDO DQG /RJDULWKPLF )XQFWLRQV SULRU WR VWXG\ LQJ WKHP DV GLĳ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ıQG D ŗGHıQLWLRQWKHRUHPSURRIŘ WUHDWPHQW EXW WKHUH LV D VXV WDLQHG HĳRUW WR LPSDUW D JHQXLQH PDWKHPDWLFDO WUHDWPHQW RI DSSOLHG SUREOHPV ,Q SDUWLFXODU RXU JXLGLQJ SKLORVRSK\ OHDGV XV WR LQFOXGH LQIRUPDO SURRIV DQG JHQHUDO FDOFXODWLRQV WKDW VKHG OLJKW RQ KRZ WKH FRUUHVSRQGLQJ FDOFXODWLRQV DUH GRQH LQ DSSOLHG SUREOHPV (PSKDVLV RQ GHYHORSLQJ DOJHEUDLF VNLOOV LV H[WHQGHG WR WKH H[HUFLVHV RI ZKLFK PDQ\ HYHQ WKRVH RI WKH GULOO W\SH DUH JLYHQ ZLWK JHQHUDO UDWKHU WKDQ QXPHULFDO FRHĴFLHQWV :H KDYH UHıQHG WKH RUJDQL]DWLRQ RI RXU ERRN RYHU PDQ\ HGLWLRQV WR SUHVHQW WKH FRQWHQW LQ YHU\ PDQDJHDEOH SRUWLRQV IRU RSWLPDO WHDFKLQJ DQG OHDUQLQJ ,QHYLWDEO\ WKDW SURFHVV WHQGV WR SXW ŗZHLJKWŘ RQ D ERRN DQG WKH SUHVHQW HGLWLRQ PDNHV D YHU\ FRQFHUWHG HĳRUW WR SDUH WKH ERRN EDFN VRPHZKDW ERWK ZLWK UHVSHFW WR GHVLJQ IHDWXUHVŠPDNLQJ IRU D FOHDQHU DSSURDFKŠDQG FRQWHQWŠUHFRJQL]LQJ FKDQJLQJ SHGDJRJLFDO QHHGV &KDQJHV IRU WKH )RXUWHHQWK (GLWLRQ :H FRQWLQXH WR PDNH WKH HOHPHQWDU\ QRWLRQV LQ WKH HDUO\ FKDSWHUV SDYH WKH ZD\ IRU WKHLU XVH LQ PRUH DGYDQFHG WRSLFV )RU H[DPSOH ZKLOH GLVFXVVLQJ IDFWRULQJ D WRSLF PDQ\ VWX GHQWV ıQG VRPHZKDW DUFDQH ZH SRLQW RXW WKDW WKH SULQFLSOH ŗDE D LPSOLHV D D RU E D Ř WRJHWKHU ZLWK IDFWRULQJ HQDEOHV WKH VSOLWWLQJ RI VRPH FRPSOLFDWHG HTXDWLRQV LQWR VHYHUDO VLPSOHU HTXDWLRQV :H SRLQW RXW WKDW SHUFHQWDJHV DUH MXVW UHVFDOHG QXPEHUV YLD WKH S ŗHTXDWLRQŘ S D VR WKDW LQ FDOFXOXV ŗUHODWLYH UDWH RI FKDQJHŘ DQG ŗSHUFHQWDJH UDWH RI FKDQJHŘ DUH UHODWHG E\ WKH ŗHTXDWLRQŘ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ŗ([SORUH DQG ([WHQGŘ FKDSWHUFORVHUV LQWR WKH ERG\ RI WKH WH[W )RU H[DPSOH WKH IXQFWLRQV WD[ UDWH W.L/ DQG WD[ SDLG 7.L/ RI LQFRPH L DUH VHHQ IRU ZKDW WKH\ DUH HYHU\GD\ H[DPSOHV RI FDVHGHıQHG IXQFWLRQV :H WKLQN WKDW LQ WKH SURFHVV RI OHDUQLQJ DERXW SRO\QRPLDOV LW LV KHOSIXO WR LQFOXGH +RUQHUŖV 0HWKRG IRU WKHLU HYDOXDWLRQ VLQFH ZLWK HYHQ D VLPSOH FDOFXODWRU DW KDQG WKLV PDNHV WKH FDOFXODWLRQ PXFK IDVWHU :KLOH GRLQJ OLQHDU SURJUDPPLQJ LW VRPHWLPHV KHOSV WR WKLQN RI OLQHV DQG SODQHV HWFHWHUD LQ WHUPV RI LQWHUFHSWV DORQH VR ZH LQFOXGH DQ H[HUFLVH WR VKRZ WKDW LI D OLQH KDV QRQ]HUR LQWHUFHSWV [ DQG \ WKHQ LWV HTXDWLRQ LV JLYHQ E\ [ \ C D [ \ DQG PRUHRYHU IRU SRVLWLYH [ DQG \ ZH DVN IRU D JHRPHWULF LQWHUSUHWDWLRQ RI WKH HTXLYDOHQW HTXDWLRQ \ [ C [ \ D [ \ %XW WXUQLQJ WR RXU ŗSDULQJŘ RI WKH SUHYLRXV ...
View Full Document