lecture211140 - † p f RV w P ` d RV TV ƒ y c ‰ d 95‡P...

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Unformatted text preview: † p f RV w P ` d RV TV ƒ y c ‰ d 95‡P x~‰ S”X ”ec x•Y™"'v r }gec d i g f RV w P ` d R y f c ` ` d T RV w P ` d |UkT r {P Y€‰ SaX aec YV 5‡P zyT ”ec YV x€‰ SaX a•l u ƒ yv vnBƒ r u tv p R Vci R g ` dc T SrPdohh'f aesYV r R PV c i R g d SqqoUhnf e’cV — p SrPdohUn‡P "0m07"H4 "‡£ a•l kDi) R V c i R gf f !  ¥ #  2  ` d & j ¡ h e c P — R X R g Pf T t “ R ` fTgf`d…T ™˜c YV hhs–•YV ”9y 6S’‘V  ‰ [email protected] †‡…ƒ¨‚  y€wxv u t RsPrqcphh'f aec BaYWUSQI HG¡ „ V i R g ` d b ` XV T R P & F # !  ¥ £ ! § ¡ ¥ #  2 $" ¨¦$$98 706354 3 1 #¤¡B#ED3BA $@( $" ¨¦$$98 706354 3 1 © ¡ C ! ) ! # !  ¥ £ ! § ¡ ¥ #  2 & ) ! & # !  ¥ £ ¡   ¡ © § ¥ £ ¡ 0% $( '% $" ¨¦¤  ¨¨¦¤¢ ‚ ”¢3y “ ’ v"'v ‘ vnB"Žu r v „ uƒy u ƒ yv ƒ p ƒ ‚ „ m‚  ~xv vnBƒ r u tv S‰ ƒ y w u ƒ yv pƒ c‰ d di g }Uƒc hkT r h‡‰ p USrPdohh'f ™˜c hxˆ HG¡ XR T R V c i R g P — X RV & F ƒ v Sw ŒBƒ r u r v ‚i ƒ ƒ …v ƒ p SxB"Žu r v „ ƒ ƒ v ¨‚ ŒBƒ r u ‹v S¢ŠhY‰ˆ p ƒ ‰ h X RV … ˆ †  † "'v r ƒy †  w • ‚  n‡p ˆ ƒ yv w † ‚ … y h ` „ ‰ R — P  P ` d R ` {qh€ƒc  xV ‚qr‡€f aec 6S’‘V  HG¡ &F ƒ RV w P d — ƒ yv ƒ p @x~‰ S”X ƒcV –v nB"Žu r v Gˆ ƒ ƒ RV w P d — ƒ yv @x~‰ S”X ƒcV –v nBƒ r u tv Sw pƒ u ƒ wv ƒ p vSxB"Žu r v {† ƒ u ƒ …v vSxBƒ r u tv ¨‚ pƒ h X RV ˆ † Šhxiy ” ˆ ’ Ÿ"'v r h¦‰ ‚  “ y v"'$p z9ž HG¡ uƒy XR u ƒ yv c ` & F † š srPqphh'f  xdcaq6qb ”ec R V c i R g RV  g T ` ` d XR h¦‰ r srPqphh'f dB”hx…› {P x€‰ SaX aƒŠ‡P SrPdo‚WeBqsxV R V c i R g œ b ` R RV f RV w P ` d c f R V c i ` T b ` c R ` d T ƒ yv aƒc YV "'zƒ r u ‹v u nv š ‡P x€‰ SaX ”™l  ˜ — – • p ƒ y f RV w P ` d ƒ yv ƒ p nB"Žu r v {† ƒ ƒ yv nBƒ r u tv ¨‚ pƒ h RV w P ŠY€‰ SaX y ˆy dƒcV — XhYV‰ˆ † R ƒy r XR u n‡p z9ž HG¡ ƒ yv c ` & F † u nv h¦‰ ‚ ± b ` c ‰ T ` c g R ` ` b d ‰ ` b ` d c T c ‰ ° ƒ Bd}Y•‚qD¢xV w 7k¤ƒc ¨kE‰ aƒsxV }gd ®Sw † X`b Š6qB` ¯ ‘ P i TV X c T b © T ‰ — R ` — V e ` d c f ‰ ` b ` d X RV ˆ ƒ G‚zqx”Qªdh¢¦™®cV ‚ad @rqhWT ae‡P ‚qE‰ aƒc hY‰{† † T ` c g R w § b ` cf R ` f6dD£YV ™™Bd0~‰ srPV  kb b ‰ g i V i ` d c f ­ ‰ ` b ‰ ` d c T ` c ‰ d c ‰ w b Pf X RV ˆ ƒ EYa7drbzŸaƒG‡P •‚qE¢aeŠ6S’‘V  }ge¬«ag e¦€s‰ hx3¨‚ †Tb`c fdBdz` w xV R X ` b g T ‰ w T X R X ` b ` ‘ P i TV X c T b © T ‰ ¡ ‰ ` ` d c b ` f 6q¤q¦‚` sYV ¥ h¦‰ 6qBS¨zqxa™ªdhQ¦™— €‚q ae¨fqc €‰ T`c g R f b` w g ` d T 6q¤£xV w ‡P B3„ h£R ”ec xV § qBad — ‡‚ i§ ’ u k–h¥ `b` “ ” ƒ§v ¦ R` G„ ‚S‘V  •hx”¦eb  [email protected]` ‡‰ ƒcV Šq‡$‡P ¥ T gV X ‰ RV X R ‰ e ¤ R d — V P f  P P e b ‰ g i V {£3¢€Ya7d’bBi ‰  xyh¦6¢“  x¢€‚q5xvf‡a¦|hq‡P R HG¡ RV T g ‰ i RV ¡ ‰ ` TV b ` ¡ R ‰ c V &F ¼ƒ  ¸ ˆv ¸ ƒ …¸ …v ¸ ƒ ‚ ¸ wv ¸ ƒ †¸ v º ƒ¨‚ Bh'‚sd¤»‚mf¤»‚SeD† Œ¢Dh r {† ƒ ¼ƒ †¸ v ¸ ƒ …¸ ˆv ¸ ƒ ‚ ¸ wv ¸ ƒ †¸ v º p ƒ ƒ{e‡‚ …‚sdh'‚mf¤»‚SeD† Œ¢¤h Ž¨‚ ± R PV c i R g ` T b ` ‘ R ` d c T · † T R PV @Sqqphh'f ‰ ydfSSxV aƒ¬Œ5fhSqqc ¯ i R g R —  P ` d c f R V c ‰ ` ` T b ` ‘ R ` d X RV & F ohh'f  xV ‚rPq‡€f aƒ¹{P srPqEYfqb ydfSSYV aƒc hY‰ˆ HG¡ †ƒ y¸ t T V‰ y'v [email protected] X ` b ` X b P f c ` ` d T p f R V c ‰ ` ¡ # © ¡ C ! ` d R ` d 6qBae¦Ÿ{P zyT aec xV ¬‡P srPqEYfqb BED3n aec 6”ec “ƒ t¸ y T V‰ X`b` XbP f c` T ay9nv [email protected] 6qBae¦v‡P BWT ‰ xV p Sqqphh'f Q˜· kDi) R PV c i R g ‰ f & j ¡ u † ¶ 6‚ U¦‰ … XR u ‚µ ´ † u w  ´ h¦‰ XR u w ” † HG¡ &F hb` dc di‰ 7fae¦P |‡‚` œ P X R g T R V c ‰ b ` e P  ‰ iV c w ` d c w w P T c ‰ d — P R ¡ SaUhW› hsrPqEeB"‡{€6xd}‰ ‚aeE‰ Ÿ` Sy9}Uec ‚a¤` ° ³ & !  ¥ £ ¡  # !  ¥ £ ! § ¡ # © ¡ C ! 30% " ¨¦¤e² $3 m~$$8 [email protected] −4 −3 −2 −4 −3 −2 −1 −1 0 1 2 3 4 0 1 2 3 4 ± R PV c i R g ` R P¯ P c¯ ` R @Sqqphh'f ”St€d»zaSP ‰ p ŒH† “ y v"'$p z9ž HG¡ T· u ƒ yv c ` & F † ` R P¯ Pc¯ ` R SaSt~q»zaSP ‰ xV vrfV ¦asP h‡rfV Sqqc Tp  R X R ‰ R PV ¯ohh'f ™YV |Yad — WeBSsxV ¦™¦Ud p srPqphh'f UBYs}U•l i R g ‰ T d iV ` T b ` ‘ R R ‰ T ‰ R V c i R g ‰ “ TV c ‰ d †cR w  XRPi` 6s6` 6r`7` hsz6yT ` ¦dT aec S7Ud [email protected] 6qBae¦P ™˜c a®qV aSt~q»zaSP xV w ‰ ` d ` ‘ ‰ T V ‰ X `b ` Xb P — P R f ` R P¯ Pc¯ ` R T p “T V‰ X`b` XbP fP c` T [email protected] 6qBae¦‡•BWT ‰ xV p SrPdohh'f ‡Ã·  ˜ — – • R Vci R g ‰ f † yv oƒ “ n‡p  u ƒ ¿ '$p 6aƒc “ y  u ¿ ÁrfV yv R ` d y “ “ y h¦‰ À™eS‚` ‚r`f` Y€‰ saX 6S’‘V  fxV }U•l X R ¿ y T c R w  RV w P R ` “ T c ‰ d † y  ‰V b ‰ c R X R e ` X R ` d c f ` g ‰ ` R  c i ‰ ¤ ƒnv r`h„€«kE‡‘¬S‚`ah6`"fahYV ”e9‡P aY€¦‘ aSP ¦do¦Up` Pdc UXhSP3y6`qy¦Bi ƒanv qh„€YqbE¦‘ s6ah‚3f”X aƒ™‡P aY€¦‘ T R e T b b P t ` ‰V ‰ c R ` X R ` e ` ` d c f ` g ‰ d‰ |i‡‚` frV Sqqpihh'f aSP‹€q¾¯paRsP ‰ xV p SrPdohUnf kDi) R PV c R g ` R ¯ P c ` T R Vci R g &j ¡ # ! ¥£ ! § ¡ –½ ¥½ ¡ $" ¨¦$$98 i! Bh6ksi! – −6 −5 −4 −3 −2 −6 −5 −4 −3 −2 −1 0 −1 1 2 3 4 5 6 0 1 2 3 4 5 6 ‚ ¨w ” ÊyÉ vn‡p HG¡ É u ƒ yv & F h ` R P¯ Pc¯ ` R {”St€d»zaSP TV T R V c i R g RV —  Pf ` d c f d i ‰ ` b ` d c ` — ` R w b ` c xhsrPqphh'f  [email protected] |¦¨HfaeBad •aYV eBqB` È †{aRst€Pd»p`”S•xV p R6”de¤“6sxV‡3e asŽªSP w }‰ xV p Sqqc ` P¯ c¯ R P T ` c c R P ` R P cT cR R PV ¯oihhg'™f‡P dg€eb  `aec ƒco6`ydf`qSRYV aYrVv€|SS7rÇk‡ad ¦‚¬˜· Rf e‰ d T i Tb c ` R  ‰cRP VbP di‰` f ¥ # ¡ ¡ ! Æ ( ¥ !   © p¤¨— [email protected] E3 Ä −4 −3 −2 −4 −3 −2 −1 −1 0 1 2 3 4 0 1 2 3 4 † ` R P¯ P SaSt~qc ¯`RP T zaS¨YV “ y ¨† v"'$p SrPdohUnf aeÌrfV aYV eBqB` È HG¡  u ƒ yv R Vc i R g ` dc ` R wb `c &F † ` R P¯ P c¯ ` R P T Ë  ‰ ‘ b ` c R R R RV T ‰ ` b i ` SaSt~q»zaS•YV ¹~¦WfqSYV ¦‰ SP  xy¦¨kp‚aX b RV T ‰ ` b i R  c iV b c T c ‰ d R V c i R g ¦P  YW‡‚kzhxV ¦doYkkªT xV }Uec SrPdohh'f  ˜ — – • −6 −5 −4 −3 −2 −6 −5 −4 −3 −2 −1 0 −1 1 2 3 4 5 6 0 1 2 3 4 5 6 †  y ’ vn‡p HG¡ u ƒ yv & F † R PV V T P w P P c c i ` e ŠSqq’cWS"e SBi dsp63yT ¯ ` d — b ` d c d i ‰ P X R g T R PV c i R gf ` T b ` ‘ R zkb e’cV ‰fae¦P ¦‚` ahhHhSqqphh'™ydfSS…·  ˜ — – • uvyƒnv ¿ Ð t‡p U¦‰ ƒ y pv X R u ƒƒ yv p vyn‡tv ¿ Ð ®{Sfgd ` ° p h`‘‰ † ¿ ¹p u r q’ckŽ— ™¤i5‡P ydfSSxV aƒsxV r ˜· Ð ` Vb ` — “ p f `Tb` ‘ R ` dc T f † T R PV c i R g ` T b ` ‘ R ` b fhSqqoUhnf ydfSSYV qE‰ ‚ ” y u "'v r h‡‰ ‚  y Î ’ u n‡p }Uƒc ‚”DÍ HG¡ Ï ƒy XR ƒ yv c ‰ d — P d & F † p f RV w P ` d R 95‡P x~‰ S”X aƒc xV y WfSzŽ¦€f ¦b` ‘` bP u ƒƒ yv p vyn‡tv r X R f RV w P ` d R U¦‰ r ‡P x~‰ S”X aƒc xV y WfSzŽ¦€f ¦b` ‘` bP u ƒƒ y v vynv r ‡p f p f R Vci R g `Tb` ‘ R qV 5‡P srPqphh'f WeBSsxV `d T aƒc xV r 6a•l ÌSrPdohh'f aS‹€q¾paSP ‰ "„ p Biž kDi) R ` d † R Vci R g ` R P¯ Pc¯` R ` c` &j ¡ # ! ¥£ ! § ¡#©¡C ! $3 m~$$8 [email protected] −3 −2 −4 −3 −2 −1 −1 0 1 2 3 4 0 ` RV ` d P c c i ` e T ` d axq aƒc qso‚3W‚kb ecV — xqkB` w iV b c `d XR aƒc h¦‰ p ‡P g~eb  aƒ–v y u f d e‰ ` dc f d e ‰ ` d c f R PV c i ` Ö ` ` d c T ‡P g€ƒb  aƒ¹‡P Sqqp6Ufkb aƒ™xV −4 1 2 3 4 †ƒ y u t w ¦ `b aªT qE‰ ¿ Ð {P g€ƒb  p f de‰ t aYrV aec d  Sk¤ƒc p `R `d gPb d p f de‰  `d l ƒ ¿ Ð ‰‡P g~eb ”™Q{† u 5‡P `  ‡‰ Õ pf R u 5‡P Y€‰ SP ¨¨‚ p f RV w È ƒ † ¿ Ð 5‡P g€ƒb  p f de‰ ` d RV TV ƒ Ó ¸ Ô c RV P ` d c  R X R ‰ aƒc Y®xHDdm¾v sx‡3e aƒrfV ¦aSP h¦irfV p SrPdohh'f aSP R Vci R g ` R ¯ P c¯ ` R P f d e ‰ ` d R T ƒ Ô ¸ Ó c RV P ~q»zaS•‡P g€eb  aƒc SP YV zexv Sx‡"e {sfUd ` ° h`‘‰ u5{»v ¿ Àp {† ƒ† Ð ƒ u ƒ Òv p ƒ ‚ h X RV vSx‡Ž¨ŽŠhY‰ˆ †‡‚ ”QÏy uvƒ"'v ¿ ¹p 6aƒ¤‡‚  y Î ’ v"'$5÷ HG¡ y Ð R` dc “ u ƒ yv p f & F # ! ¥£ ! § ¡#©¡ C ! j # ¥©¡ 4  $" ¨¦$$8 BED3BA 3 ¤¡ ¨‚¤H3¨© Ñ † u ƒƒ y Ð pv 9y Ÿk"'v ¿ Àt‡p X hR¦‰ y u k"'$‹v ƒƒ yv p c ‰ d ¦fV b ` † ‰ T b ` ` iV X R ¿ Ð p }gec 0qkBŸÝ aqeBS‘ zYD‘ h¦‰ p f‡P `  ‡eb aƒc YV ¿ Ð p ‡P Y€‰ saX aƒc }Uƒc e6”™I {´ R‰ `d T f RV w P ` d c ‰ d ¡ i ` d ƒ †ƒ y nv ¿ Ð p u t R PV c i R g V i  e ¤ ` d RV ‰ c „ P b P `  P Í ƒ Sqqphh'f cBxrVU¤p` aec Y€ƒa{P dc t ¦€f S’‘‡£ŽGˆ † XR t h¦‰ y 6r`U€YqE¦‘ aec `  ‡U|eBqsŒQSw T  „ ‰V b ‰ ` d R ‰ dib`c R· ƒ †ƒnv‡p ¦€f Sqq}g£6` aƒc YV t ƒcV ®"'$p z‡Yh7` Q{† y b P R PV c ‰ g Ü ` d R d — ƒ yv ` i ‰ e Õ ƒ † ` R P¯ P c¯ ` R P TV ƒ yv R V c i R g ` b g ` ¡ Û ƒ SaSt~q»zaS•YQ"'$p SrPdohUnf kakT ‡€‰ Q¨‚ ÚÆÆ ( £ ( © Ù ¡ [email protected]@m$D× Æ Ø $"0m~$$8 [email protected] in$$n 8 # !  ¥ £ ! § ¡ # © ¡ C ! × ! ) ! −4 −3 −2 −1 −4 −3 −2 −1 0 1 2 3 4 0 1 2 3 4 † ` T b ` ‘ RV T V f SWeBSSY•e’c$‡P d e ‰ ` d d ic ` ¡ Í † ƒ yv g~eb  aec |eB‡£®n‡p u Š‡P @€eb  aec 6s‘V  HG¡ t f de‰ `d R` &F † ƒ yv p f n‡5‡P `  ¦ƒb aec hY‰¨„ R ‰ ` d X RV ˆ ƒ †ƒ y o"'v ¿ Ð p hY‰¨S‰ X RV ˆ ƒ wy † ‚ ” E† vn‡p srPqphh'f aSt~q»zaSP 6S’‘V  HG¡ &F y u ƒ yv R Vc i R g ` R P¯ Pc¯ ` R R ` w u ƒ yv p f ` T b ` ‘ R ` d X RV & F †Sr`hqVWqTSP3e‡qV „T f y  ˆ v"'$5{P WeBSSYV ”ec hxˆ HG¡ −4 −3 −2 −4 −3 −2 −1 −1 0 1 2 3 4 0 1 2 3 4 † ‡‚  y ’ v"'$5{P WeBSSYV ”ec hxˆ HG¡ u ƒ yv p f ` T b ` ‘ R ` d X RV & F ...
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This note was uploaded on 06/09/2011 for the course MAC 1140 taught by Professor Williamson during the Summer '08 term at University of Florida.

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