prob3 - q<e<!Wp €!Wp =Wyzei7yqO!3 7]yeW]e m...

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Unformatted text preview: q<e <!Wp €!Wp =Wyzei7yqO !3 7]yeW]e m qe]<W!N!pO y7q ddd ZR$t‚RR 7s$R${R _„BAj‚8 7Y‚‚ n d qY‚ PBjjBb$t }„BAsA$j$k I$R„$AZ$Bt BP Y‚ 8BtYjk $t{B8‚R w? $t cd(((D BP s{{BZt ‚-‚{T Z$%‚R YsR A‚‚t ‚R$8s‚I PB„ s A$ s{{BZt$t h„8 ? d1 d; 1( 11 n( €w?D dx dx ; 1 d wsD 3$tI Y‚ ‚-}‚{‚I %sjZ‚ stI Y‚ RstIs„I I‚%$s$Bt BP Y‚ 8BtYjk $t{B8‚R wAD V „stIB8 Rs8}j‚ BP E; ‚-‚{Z$%‚R $R s,‚t GYs $R Y‚ }„BAsA$j$k Ys Y‚ Rs8}j‚ 8‚st %sjZ‚ ‚-{‚‚IR c1(x((2 1 qY‚ j$P‚ BP s t${,‚jT{sI8$Z8 As‚„k }„BIZ{‚I Ak s 8stZPs{Z„‚„ $R tB„8sjjk I$R„$AZ‚I b$Y s 8‚st BP 1( YBZ„R stI s RstIs„I I‚%$s$Bt BP ; YBZ„R wsD GYs }„B}B„$Bt BP As‚„$‚R Ys%‚ s j$P‚ BP j‚RR Yst dx YBZ„R2 wAD qY‚ 8stZPs{Z„‚„ $R {BtR$I‚„$t s bs„„stk PB„ Y‚ As‚„k <Bb 8stk YBZ„R BP ZR‚ RYBZjI Y‚ bs„„stk {B%‚„ RB Ys x0 BP Y‚ As‚„$‚R Ys%‚ B A‚ „‚}js{‚I2 w{D 7Z}}BR‚ Ys s As‚„k b$Y j$P‚ BP j‚RR Yst dx YBZ„R $R {BtR$I‚„‚I B A‚ I‚P‚{$%‚ yP M As‚„$‚R s„‚ R‚j‚{‚I s „stIB8 P„B8 s js„‚ As{Y bYs $R Y‚ }„BAsA$j$k Ys s 8BR 1 As‚„$‚R s„‚ I‚P‚{$%‚2 n 7Z}}BR‚ Y‚ R{B„‚ BP Y‚ y7q ddd 8$IT‚„8 ‚-s8 $R s tB„8sj „stIB8 %s„$sAj‚ b$Y 8‚st Ex stI RstIs„I I‚%$s$Bt d( qY‚ $tR„Z{B„R I‚{$I‚ B B&‚„ ; „sI‚R B Y‚ RZI‚tR qY‚ A‚R „BZ} ‚ VR Y‚ R‚{BtI A‚R „BZ} ‚ R Y‚ Y$„I A‚R „BZ} ‚ ]R stI Y‚ bB„R „BZ} ‚ *R !tjk x0 BP Y‚ RZI‚tR ‚ VR stI d(0 BP Y‚ RZI‚tR ‚ *R wsD ]sj{Zjs‚ Y‚ {ZTB& R{B„‚ PB„ Y‚ „sI‚ "V" wAD yP b‚ Rs8}j‚ x RZI‚tR $tI‚}‚tI‚tjk P„B8 Y‚ {jsRR bYs $R Y‚ }„BAsA$j$k Ys Y‚„‚ $R s j‚sR Bt‚ RZI‚t ‚$t s "*"2 w{D yP b‚ Rs8}j‚ d(( RZI‚tR $tI‚}‚tI‚tjk P„B8 Y‚ {jsRR bYs $R Y‚ }„BAsA$j$k Ys Y‚„‚ s„‚ 8B„‚ Yst M RZI‚tR ‚$t st "V"2 w<$tU ZR‚ WB„8sj V}}„B-$8s$BtD wID 7Z}}BR‚ Y‚ $tR„Z{B„R I‚{$I‚ B Ps$j YBR‚ RZI‚tR bYB R{B„‚ j‚RR Yst ;( $t Y‚ 8$IT‚„8 ‚-s8 yP b‚ Rs8}j‚ M( RZI‚tR $tI‚}‚tI‚tjk P„B8 Y‚ {jsRR bYs $R Y‚ ‚-}‚{‚I tZ8A‚„ BP RZI‚tR bYB Ps$j Y‚ 8$IT‚„82 ; 3B„ s {‚„s$t s}$ZI‚ ‚R $ $R ,tBbt P„B8 }sR ‚-}‚„$‚t{‚ Ys R{B„‚R s„‚ I$R„$AZ‚I tB„8sjjk b$Y st s%‚„s‚ BP ) Ex( stI s RstIs„I I‚%$s$Bt BP  ) d1 yP s „stIB8jk R‚j‚{‚I $tI$%$IZsj s,‚R Y‚ ‚R bYs $R Y‚ }„BAsA$j$k Ys Y$R R{B„‚ b$jj j$‚ $t Y‚ $t‚„%sj En( B EM(2 VRRZ8‚ Y‚ {Z„„‚t }B}Zjs$Bt I$R„$AZ$Bt $R $I‚t${sj B Ys BP }„‚%$BZR }B}Zjs$BtR d x qY‚ }„B`‚{ BP }jstt$t stI R{Y‚IZj$t Y‚ AZI‚ „‚JZ$„‚R s R‚JZ‚t{‚ BP sR,R $t{jZI$t PB„‚{sR$t I‚8stI }„‚}s„$t Y‚ }„BIZ{$Bt R{Y‚IZj‚ ‚R$8s$t {BRR stI }„‚}s„$t Y‚ AZI‚ _„B`‚{ R{Y‚IZj‚„R Ys%‚ PBZtI Ys Y‚ $8‚ „‚JZ$„‚I B {B8}j‚‚ s AZI‚ $R tB„8sjjk I$R„$AZ‚I b$Y s 8‚st BP M IskR stI s RstIs„I I‚%$s$Bt BP 1 IskR qB s„„st‚ htst{$t s Y‚ {Z„„‚t „s‚ BP $t‚„‚R Y‚ „‚sRZ„‚„ 8ZR ,tBb Y‚ AZI‚ b$Y$t x IskR BP A‚$tt$t Y‚ }„B{‚RR !Y‚„b$R‚ s }‚tsjk b$jj A‚ $8}BR‚I Ak Y‚ Ast, wsD GYs $R Y‚ }„BAsA$j$k Ys s AZI‚ $R ht$RY‚I b$Y$t x IskR2 wAD <Bb 8stk IskR s„‚ t‚{‚RRs„k RB Ys Y‚„‚ $R x0 {Yst{‚ B {B8}j‚‚ s AZI‚ b$Y$t Ys tZ8A‚„ BP IskR2 w{D 7Z}}BR‚ d( AZI‚R Ys%‚ B A‚ R{Y‚IZj‚I GYs $R Y‚ }„BAsA$j$k Ys s j‚sR M AZI‚R b$jj A‚ RZA`‚{‚I B s }‚tsjk2 E V 8stZPs{Z„‚„ RZA8$R s %‚„k js„‚ As{Y BP $‚8R }‚„ b‚‚, B s „‚s$j‚„ qB 8Bt$B„ JZsj$k {Bt„Bj Bt ‚s{Y As{Y Y‚ „‚s$j‚„ sIB}R s bBTRs‚ Rs8}j$t }jst PB„ I‚{$R$Bt 8s,$t yt Y‚ h„R Rs‚ s Rs8}j‚ BP d( $‚8R $R „stIB8jk R‚j‚{‚I P„B8 Y‚ As{Y qY‚ As{Y $R s{{‚}‚I $P Y$R Rs8}j‚ {Bts$tR tB I‚P‚{$%‚ $‚8 stI $R „‚`‚{‚I $P Y‚ Rs8}j‚ {Bts$tR bB B„ 8B„‚ I‚P‚{$%‚ $‚8R yP Y‚ Rs8}j‚ {Bts$tR Bt‚ I‚P‚{$%‚ $‚8 Y‚t Y‚ As{Y $R ‚R‚I $t Y‚ R‚{BtI Rs‚ $t bY${Y s t‚b Rs8}j‚ BP x( $‚8R $R „stIB8jk R‚j‚{‚I yP Y$R R‚{BtI Rs8}j‚ {Bts$tR j‚RR Yst x I‚P‚{$%‚ $‚8R Y‚ As{Y $R s{{‚}‚I !Y‚„b$R‚ Y‚ As{Y $R „‚`‚{‚I 7Z}}BR‚ Y‚ }„B}B„$Bt BP I‚P‚{$%‚ $‚8R $t s As{Y $R ((M stI ‚s{Y As{Y $R RB js„‚ Ys Y‚ ‚R Rs8}j‚R s„‚ Btjk s $tk }s„ wsD yt Y‚ h„R Rs‚ BP Rs8}j$t bYs $R Y‚ }„BAsA$j$k Ys s $%‚t As{Y $R s{{‚}‚I2 wAD yt Y‚ h„R Rs‚ BP Rs8}j$t bYs $R Y‚ }„BAsA$j$k Ys s $%‚t As{Y $R „‚`‚{‚I2 w{D 7Z}}BR‚ Ys s $%‚t As{Y $R $tR}‚{‚I $t Y‚ R‚{BtI Rs‚ bYs $R Y‚ }„BAsA$j$k BP s{{‚}$t Y‚ As{Y2 w<$tU ZR‚ tB„8sj s}}„B-$8s$BtD wID 3$tI Y‚ }„BAsA$j$k Ys s $%‚t As{Y b$jj A‚ „‚`‚{‚I w‚D GYs $R Y‚ s%‚„s‚ tZ8A‚„ BP $‚8R $tR}‚{‚I }‚„ As{Y2  3„B8 }sR Iss $ $R ,tBbt Ys (0 BP A„stI V {B8}Z‚„ ZR‚„R }jst B AZk s t‚b‚„ 8BI‚j BP A„stI V {B8}Z‚„ $t Y‚ PZZ„‚ 7Z}}BR‚ 1x A„stI V {B8}Z‚„ ZR‚„R s„‚ $t‚„%$‚b‚I PB„ Y‚$„ PZZ„‚ A„stI }„‚P‚„‚t{‚ =R‚ tB„8sj s}}„B-$8s$Bt B htI wsD Y‚ {Yst{‚ Ys s j‚sR d( BP Y‚R‚ ZR‚„R $t‚tI B Rb${Y A„stI $t Y‚$„ t‚- {B8}Z‚„ }Z„{YsR‚ wAD Y‚ {Yst{‚ Ys ‚-s{jk d( BP Y‚R‚ ZR‚„R $t‚tI B Rb${Y A„stI $t Y‚$„ t‚- {B8}Z‚„ }Z„{YsR‚ M istIB8jk R‚j‚{ s tZ8A‚„ P„B8 Y‚ AB- b$Y tZ8A‚„R T1T1T1 ( 1 1 stI Y‚ tZ8A‚„ BAs$t‚I $R Y‚ s8BZt BP IBjjs„R kBZ b$t wB„ jBR‚D wsD _jsk Y‚ s8‚ Bt{‚ ? ) ' BAs$t‚I 3$tI Y‚ }„BAsA$j$k I$R„$AZ$Bt BP ? wAD 3$tI Y‚ ‚-}‚{‚I %sjZ‚ stI Y‚ 7* BP ? w{D _jsk Y‚ s8‚ n( $8‚R ZR‚ tB„8sj s}}„B-$8s$Bt B htI Y‚ {Yst{‚ Ys kBZ b$jj A‚ $t Y‚ „‚I w$‚ jBR$t RB8‚ 8Bt‚kD 1  qY‚ }„BAsA$j$k I$R„$AZ$Bt PB„ Is8s‚ {js$8R w? $t cd(( $‚ ? ) d( 8‚stR Ys Y‚ Is8s‚ {js$8 $R cd(((D }s$I Ak st sZB8BA$j‚ $tRZ„st{‚ {B8}stk Bt {Bjj$R$Bt $tRZ„st{‚ $t dM $R RYBbt A‚jBb ? ( ; d( 1( ;( E( €w?D ( (; (n (d (d (d wsD 3$tI Y‚ ‚-}‚{‚I %sjZ‚ stI Y‚ RstIs„I I‚%$s$Bt BP Y‚ Is8s‚ {js$8R $t dM wAD V „stIB8 Rs8}j‚ BP (( Is8s‚ {js$8R $R s,‚t GYs $R Y‚ }„BAsA$j$k Ys Y‚ Rs8}j‚ 8‚st %sjZ‚ ‚-{‚‚IR c1((2 w{D qY‚ $tRZ„st{‚ {B8}stk I‚{$I‚I Ys $P Y‚ {Z„„‚t {js$8 $R j‚RR Yst cdx(( $ b$jj A‚ $t{„‚sR‚I Ak 1(0 $t d !Y‚„ Is8s‚ {js$8R b$jj A‚ Zt{Yst‚I GYs bBZjI A‚ Y‚ ‚-}‚{‚I %sjZ‚ BP Y‚ Is8s‚ {js$8R $t d2 d( VRRZ8‚ Ys Y‚ 8BtYjk Rs„$t Rsjs„k BP Y‚ Zt$%‚„R$k „sIZs‚R $t dM $R tB„8sjjk I$R„$AZ‚I b$Y s 8‚st BP cd;((( stI s RstIs„I I‚%$s$Bt BP c1((( wsD GYs }‚„{‚ts‚ BP „sIZs‚R Ys%$t 8BtYjk Rsjs„k A‚b‚‚t cdd((( stI cdx(((2 wAD 7Z}}BR‚ Ys s }‚„RBt Ys%$t Rsjs„k A‚b‚‚t cdd((( stI cdx((( $R ‚j$$Aj‚ PB„ `B$t$t s YBZR$t jBst R{Y‚8‚ B&‚„‚I Ak s Ast, yP x( „sIZs‚R s„‚ R‚j‚{‚I s „stIB8 P„B8 s js„‚ Zt$%‚„R$k bYs $R Y‚ }„BAsA$j$k Ys Y‚„‚ s„‚ 8B„‚ Yst 1 ‚j$$Aj‚ „sIZs‚R2 dd qY‚ 8BtYjk Rsj‚R BP *s„,Tst qBBY}sR‚ s„‚ A‚j$‚%‚I B A‚ tB„8sjjk I$R„$AZ‚I b$Y s 8‚st BP d((( ZA‚R stI s RstIs„I I‚%$s$Bt BP dx( ZA‚R wsD GYs $R Y‚ }„BAsA$j$k Ys 8B„‚ Yst dd(( ZA‚R b$jj A‚ RBjI $t Y‚ t‚- 8BtY2 wAD qB Ys%‚ s x0 }„BAsA$j$k Ys Y‚ {B8}stk b$jj Ys%‚ RZ^{$‚t RB{, B {B%‚„ Y‚ 8BtYjk I‚8stI YBb 8stk ZA‚R RYBZjI A‚ }„BIZ{‚I2 w{D GYs $R Y‚ }„BAsA$j$k Ys Y‚ Bsj Rsj‚R $t Y‚ t‚- k‚s„ $R B%‚„ d1E(( ZA‚R2 VRRZ8‚ Ys Y‚ Rsj‚R BP Y‚ d1 8BtYR s„‚ $tI‚}‚tI‚t d1 ]B8}st$‚R Ys }Z„{YsR‚ }s„R P„B8 RZ}}j$‚„R BP‚t R}‚{$Pk Y‚ 8s-$8Z8 sjjBbsAj‚ }„BT }B„$Bt BP I‚P‚{$%‚ }s„R istIB8 Rs8}j$t $R ZR‚I B I‚{$I‚ bY‚Y‚„ Y$R j$8$ YsR A‚‚t ‚-{‚‚I‚I 7Z}}BR‚ Y‚ 8s-$8Z8 sjjBbsAj‚ }„B}B„$Bt I‚P‚{$%‚ PB„ s }Z„{YsR‚ BP {B8}Z‚„ {Y$}R $R ((n Vt $tR}‚{$Bt }jst YsR A‚‚t I‚%$R‚I AsR‚I Bt s „stIB8 Rs8}j‚ BP n(( {Y$}R yP n0 B„ 8B„‚ I‚P‚{$%‚ {Y$}R s„‚ PBZtI w$‚ €  ((nD Y‚ ‚t$„‚ jB $R I‚‚8‚I Zts{{‚}sAj‚ | stI $R $tR}‚{‚I $t $R ‚t$„‚k s Y‚ RZ}}j$‚„:R ‚-}‚tR‚ 7Z}}BR‚ s As{Y BP d(((( {Y$}R {Bts$tR d0 I‚P‚{$%‚ {Y$}R wY$R bBZjI A‚ Zt,tBbt B ABY RZ}}j$‚„ stI }Z„{YsR‚„ R$t{‚ Y‚ As{Y YsR tB A‚‚t $tR}‚{‚ID WB‚ Ys Y$R $R st s{{‚}sAj‚ }„B}B„$Bt BP I‚P‚{$%‚R wAD 3$tI Y‚ }„BAsA$j$k Ys Y‚ jB b$jj A‚ I‚‚8‚I Zts{{‚}sAj‚ $‚ _w €  ((nD | w{D WBb RZ}}BR‚ Y‚„‚ s„‚ h%‚ js„‚ As{Y‚R ‚s{Y {Bts$t$t d0 I‚P‚{$%‚ {Y$}R GYs $R Y‚ }„BAsA$j$k Ys ‚-s{jk bB As{Y‚R b$jj A‚ I‚‚8‚I Zts{{‚}sAj‚2 n wsD 3$tI Y‚ 8‚st stI Y‚ %s„$st{‚ BP Y‚ Rs8}j‚ }„B}B„$Bt € | dn VRRZ8‚ Ys Y‚ p„sIZs‚ sts‚8‚t VI8$RR$Bt q‚R wpVqD R{B„‚ BP s RZI‚t $R tB„8sjjk I$R„$AZ‚I b$Y s 8‚st BP xM( stI s RstIs„I I‚%$s$Bt BP M( wsD GYs $R Y‚ }„BAsA$j$k Ys s RZI‚t R{B„‚R 8B„‚ Yst E(( $t Y‚ pVq2 wAD 7Z}}BR‚ Ys RZ{{‚RRPZj s}}j${stR BP st  V }„B„s8 s„‚ „‚JZ$„‚I B s,‚ Y‚ pVq stI R{B„‚ 8B„‚ Yst E(( yP Y‚ }„B„s8 „‚{‚$%‚R ( s}}j${s$BtR bYs $R Y‚ }„BAsA$j$k Ys 8B„‚ Yst ;( s}}j${stR Rs$RPk Y‚ „‚JZ$„‚8‚t2 VRRZ8‚ Ys ‚s{Y BP Y‚ ( s}}j${stR YsR s,‚t Y‚ pVq Bt{‚ d; V „‚s$j‚„ „‚{‚$%‚R d(( jBR BP ‚j‚{„Bt${ {sj{ZjsB„R P„B8 s RZ}}j$‚„ es{Y BP Y‚ jBR {Bts$tR s js„‚ tZ8A‚„ BP {sj{ZjsB„R qB $t%‚R$s‚ Bt Y‚ JZsj$k BP s jB s Rs8}j‚ BP 1( {sj{ZjsB„R $R R‚j‚{‚I „stIB8jk P„B8 ‚s{Y jBR qY‚ „‚s$j‚„ I‚{$I‚R B s{{‚} s jB $P Y‚„‚ s„‚ j‚RR Yst n I‚P‚{$%‚ {sj{ZjsB„R $t Y‚ ‚R‚I Rs8}j‚ VRRZ8‚ Ys Y‚ }„B}B„$Bt BP I‚P‚{$%‚ $‚8R $R ((x wsD GYs $R Y‚ }„BAsA$j$k BP s{{‚}$t s R$tj‚ jB2 wAD p$%‚t Ys Y‚ „‚s$j‚„ s{{‚}R s jB bYs $R Y‚ }„BAsA$j$k Ys j‚RR Yst 1 I‚P‚{$%‚ {sj{ZjsB„R s„‚ BAR‚„%‚I2 w{D yP Y‚ $tR}‚{$Bt R{Y‚8‚ $R s}}j$‚I B sjj Y‚ d(( jBR bYs $R Y‚ }„BAsA$j$k Ys 8B„‚ Yst Mx jBR s„‚ s{{‚}‚I2 dx V ‚j‚%$R$Bt wqzD }„BIZ{‚„ Zs„st‚‚R $R qz PB„ n k‚s„R !t ‚s{Y qz $ 8s,‚R s }„Bh BP cdx(( <Bb‚%‚„ Y‚k 8ZR }sk cx((( PB„ stk „‚}js{‚8‚t ZtI‚„ Y‚ Zs„st‚‚ yP Y$R „‚}js{‚8‚t sjRB AZ„tR BZ b$Y$t n k‚s„R BP }Z„{YsR‚ Y‚k s„‚ tB {B88$‚I B s R‚{BtI „‚}js{‚8‚t VRRZ8‚ Ys Y‚ j$P‚$8‚ BP Y‚ qz $R tB„8sjjk I$R„$AZ‚I b$Y s 8‚st BP ;1 k‚s„R stI s RstIs„I I‚%$s$Bt BP dM k‚s„R wsD GYs $R Y‚ }„BAsA$j$k Ys s qz YsR B A‚ „‚}js{‚I b$Y$t Y‚ }‚„$BI BP Zs„st‚‚2 wAD GYs $R Y‚ ‚-}‚{‚I }„Bh }‚„ Rsj‚ wt‚ sP‚„ }sk$t PB„ s }BRR$Aj‚ „‚}js{‚8‚t ZtI‚„ Y‚ Zs„st‚‚D2 w{D qY‚ }„BIZ{‚„ bstR B $t{„‚sR‚ Y‚ ‚-}‚{‚I }„Bh }‚„ Rsj‚ B cx(( Ak „‚IZ{$t Y‚ }‚„$BI BP Zs„st‚‚ $ GYs RYBZjI A‚ Y‚ }„BAsA$j$k $t wsD $t B„I‚„ B k$‚jI Y‚ I‚R$„‚I s%‚„s‚ }„Bh2 $$ qB s{Y$‚%‚ Y‚ Bsj bYs RYBZjI A‚ Y‚ }‚„$BI BP Zs„st‚‚2 ; ...
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This note was uploaded on 02/27/2010 for the course ISOM ISOM111 taught by Professor Anthonychan during the Spring '09 term at HKUST.

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