lecture231140(1) - ‘ Y Q H h Ž C –h...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ‘ Y Q H h Ž C –h iQgfEwCIFafierE—h’ y Š V   ‡‡awYH ƒ   e‹ Yi—QgEwCHI¦&iherŽEhh t Š aPH ƒ —¨ QfF C – Œ VY ‹ fC SQ ˆ € ŠV tUTewq‚awYH ƒ „ ‰ˆ ‡‡¡ ` $† ` Hf {fF ` €}VY Ph &egY t¦…Ph ~aPH ƒ „ wXeitgPiƒpjiW UTQ ‚€ tU0xe{ hh h S – f Yh Q FH C C S  { C f  C – { f € } V Y ƒ  €y f CQ h – t¦F ~aPH „‚6bx Eik&QpW y hh  | ƒ … taF z ‰ … ixeS y {f CWC ˆ ¡ A ) ¡ 3  !  ¥ £ ! § £ 4 3 ¥ © ) ' C S $ n 0… x0wv u9¥ t¥ " ¨¦55sn 6 5¨2Ig(0 r e—q po¡ m l f h Q D f r C – W C i f f – F h ˆ C f Y˜ Y Q˜ C f Y –h  €y C D f RgwYvut6` kvjgghh ¦F ¦gS fQUeUgdIv™”eg—“•‚6bx ”t“h ’ −2 −1 −5 −4 −3 −2 −1 0 1 2 3 4 5 0 1 2 3 4 5 6 7 8 ‘ a ‰ … ˆU†‡… ƒ„‚6ybx [email protected] 0IT¦V UTRPIGEC B € h r h f Y X c C ` S X F W C S Q HH F D A !  ¥ £ ! § £ 4 3 ¥ © ) '  5@ 98557 6 5¨2100(¢ &%# " ¨¦¤  ¨¨¦¤¢ $ ! ¥£¡   ¡© §¥£¡ z ¨ V { f F   y ¨ V H ‘ C Q F rH F i $ † ¤awYH t¦®¨ ­aoawY¬giƒghI¦™§ ‡‡¡ ‹ŠV H ‡ewY– « z©  zazaE ª¢ V H  y ewY– ‘ œ — ewY–gœ VH  — ewY–e‹ VH ‹œ¨V H  e¤ewY–¨ ‘ C Q F rH F i $ † giƒghI¦™§ ‡‡¡ ¦ Ÿ š‘ ‘ ˜ ¥¤v¦„‘ v¦ ` hh tT&Qp1ŸewYH hh i&QpW “ ‡‡¡ £¢¡ •WY D • S hWF V f C h $† ‹ ™¨ ž I™IoewY–e‹ ƒ € œy  V H  ‹ œ š ¤a›Œ¤z  ™  g~ewY–¨ ˜ y—V H  ‘ [email protected] hh i&QpW “ ‡‡¡ • W Y` H Fh Q f C f Y X c f C h $† z ‰ ¦ ` € WY «¤ VH  ewY–e‹ ¿ ¾» ‹  v— uv½¹¸ ®¨ ‘ C Q F rH F i $ † giƒghI¦™§ ‡‡¡ ƒ † uvº¹… ¼» ¸ [email protected] •trf·HIF¨pWHPIF W¦ ` – CH Y ƒ † … } aPH VY A ¡ ¥ © ¡ °  e29Eo¬¶9© ¯ [email protected] ‘ ¡A©¡µ !³ ƒ ²oewY–gœ …}V H ƒ •oewY–e‹ }V H l ez ‰ tjhh 1—q €ˆ– QFS ƒ € ftCeS±Q € } ewYH ƒ „ P1TPIGEC –¨ V `h Q F S Q HH F D B  A 5¨21g((¢ @ ¤¡ [email protected] ¯ 4 3 ¥ © ) '  n A  ¥ © ¡ °  −5 −4 −3 −2 −2 −1 −1 0 1 2 3 4 3 4 5 0 1 2 3 4 5 6 7 8 {taF f † þ V € ÄewYH ƒ „ ƒ „ ‘ y [email protected] UTQ gY ÂT”C ’ ‡‡¡ HC € –C c C S f SDQ Á $ † ‹ −2 −1 −5 −4 −3 −2 −1 0 1 2 5 0 1 2 3 4 5 6 7 8 € ¨ ewYH ƒ „ V {t¦F † ‹ ƒ „ ‘ y [email protected] UTQ gY ÂT”C ’ ‡‡¡ f HC € –C c C S f SDQ Á $ † !  ¥ £ ! § £ 4 3 ¥ © ) '  ) n 3 ° ) " ¨¦55w7  5921g((¢ —@ bg9© À −4 −3 −2 −4 −3 −2 −1 −1 0 1 2 3 4 0 1 2 3 4  ¨ ž sy — awYH ™"s5x gI±W Ï ‡‡¡ € V ƒ  €y S X F $† … È { fF  …Ȑ  a  ta´¤vaÎy Í…Íz ‰… Èz ¨jeÌy z ƒ „ ÌIÉggGwËpaY Ê ‘H FQ f Y hW  ɤ™y ÇÈ z  ÉÈ Ç ­y Ç  † … ™"s¨wqx ƒ  €y ¢ Æ SgI±¦V [email protected] X F W f Y – Q fh Y `wh ehk¦EidEe{ V fh – F C W D C `Ph ehk¦Eidt“h V fh – F C W D f Q XCDWCQf eG”vjig“h C YQ • – iQ8veX U­¦F CVfF ae¦±W fh • Y “IF Ÿe{ € } awYH ™"s5x V ƒ  €y ‘ † … ™‚69w·x taF € } aPH ™‚6bx p10X gY Å ƒ  €y ¢ Æ { f V Y ƒ  €y CW F • ‹ lX geœ ‘ qsy € } aPH ™‚6b‡@ bg9¶' u¨w@ ¤¡ [email protected] ¯ V Y ƒ  €y x n 3 ° ) © ¡ 3 ¥ n A  ¥ © ¡ °  −6 −5 −4 −3 −2 −4 −4 −5 −5 −6 −6 −2 −2 −3 −3 −1 0 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 0 −1 0 −1 1 2 3 4 5 6 0 4 4 3 3 2 2 1 1 6 6 5 5  qe‹  6uhH ™‚6bx ž €y f ƒ  €y  ¡ € f ƒ  €y $ † hH ™‚6bx ‡‡¡ Ø × Ö ¡ T— E† ¨ 8ÔÓ¸ ®¨ ‘ C Q F rH F i $ † giƒghI¦™§ ‡‡¡ fH  h’e‹ ƒ™ † Õy·fhH ¡ ƒ † ÔÓt¡ ¸ ‘ A ¡ ¥ © ¡ °  ¦e29Eo¬¶9© ¯ [email protected] ¡A©¡µ ! ƒ ¡ “H f ƒ ‘ V f HH Y C S C Q te“h y wYPa”` e±Q i8Y ` Hf {fF ` € f Ph &egY t¦…Ph ®hH ƒ €  ewYH ƒ V !  ¥ £ ! § £ 4 3 ¥ © ) '  r ) © § ¥ " ¨¦55w7  5921g((¢–0¨9U) Ñ u3 ¡ f hH Ò „ Ð Þ Ä‚€ ™·“Ýœ ‡‡¡ ƒ ‹y fH $ † ‘ ƒ † — ¡ ‡‡¡ $† ‹  ƒ™¨ ž I™y ¨ aPH ‡‡¬u¦ ` g&iaY ’ €œ VY $ †¡ ‘€ WY C H A !  ¥ ) § 5"29UuÜ Û 6 5¨2100(¢ £ 4 3 ¥ © ) '  ƒ z t Ú awYH V  ƒ aaet ewYH zzzz V ƒ t awYH zV ƒ  ewYH V ‘ C Q F rH F i $ † giƒghI¦™§ ‡‡¡ © w`h &egY t¦…Ph ¢ewYH ƒ € ª¢ ewYH ƒ „ Hf {fF ` € V V !  ¥ £ ! § 4 3 ¥ © ) '  ! "298557 5921g((¢ " 4 @ Ù 4 êC hW Y {CQ •WC C 9g&ip¤{ iQ tvk&Qh [email protected] @€ Q¦ef hUgei– i¦Y • ¦Y å ¦²aY Á “pW F T&Qh y Igtho&iet“h ¦F Y {H r Y S C W W z ‹ ` –h S H F r {h h { f f Q1TQ tvƒ±Î– y “H eT…Pˆ é è F T&Qh y tai1ÂD @€ jgfii¤{ F S – C Q F Q F C S Q `h S {CVWF S C WC hW F hUgeiÝaegxhIF oPt™aY gPiƒ±pgE”tgxD ƒS y ’ç gœ {H r Y S – H Y S Y DH { Y YH € ` f Yh Q F W Q f C D f Y Q F Q l Œ l z H Y S Y DH { Y H S ¤a›z¤uaUg”“IF ¤wYt€ ±fQh y xŸfipe{ …eY Á hiW eTQ t“Ý•e‹ W C h W F ` –h C S { fh æ  l {fˆ @ä t(e ¦ ƒ sy Á “pW g¦ ¦F hTfQUpEpW B –h å f fh – H r – C ‹ l ` { Y H C S fh H Y S Y DH F ` f h Q F W Q f C D f Y F `ˆ  e›z¤zÄaY owY€ e±Q “aegxhIÄaY gwYvƒTigtxtg”D ¢ª—¨ lQ f FQ– f Y Eg¦É­tŸ”D F hh ä f¦F oYPt€ eS±Q hwaYeŸ”h8¬aY ŸwYi1TpŸt”g”D UTQ – { { YH C fh H S Y DH F ` f h Q F W Q f C D f Y C S – hh € ehoi&p¤{ PwHeS y gte“”DG¦F f¦F e“ojS aY [email protected] ˆ V fh h W C h Q f C {h D V fh i F `  Q f C D W C F ¦Ìy Á “pW e±Q “h â CixeS y † 9¡ ‘ ƒ â per v¦ ` e±Q iQ – F –h C S – WC ã FH • W Y C S Y Ve“evaY”jaF {oPt€á–GjgfiiW¤{ F hh‡aUSg”“HI`aY gPiƒ±pgE”tŸ”D fh { W D D Y YH à W C h f H Y Y D F f Yh Q F W Q f C D f Y C Y C Q FH W –h Q C {h D D W FH r h S eS±Q iQ {tvƒ“GCp5h²gfEehxj¦F‡I“eGDheECgi F0`aY Á hi•e—q ‡‡¡ –h W C S $ † A !  ¥ ) £r ° 5@ 9U¦66b5° ß ê QWF { f e‹ k10X t¦F  ì1(X hh [email protected]{ aY [email protected] tf eTQ tjC y [email protected] wXeitgPiQ Q W F f –H C h D C ` W C • r C S f C Q C h S – f Yh ˜9“GpW eTQ “h ƒS “ o‹ ìI0X “h ªfQktEig“h e±Q ¦F ƒEi¦V FH C C S – Q F l QWF f  h– fCQ f C S – QFCW – – •h z z – Q W F f { f r Y – `  h – f C Q f C S  ¦F EC “iQ at hh  ì1(X “h tgkîaY ª&QìtEig“h e—q gœ lWCQ CWF r Ž WC X –QQ txv”C • i1i– [email protected] y ~t–aY ‰fQkttvghh ¦F Æ z `  h– fCQ f f S ±fQh y tgk– ‚e…hj"w€”Ee"a¬x"€ t¨ ~UTîehh vjixC 5e‹ { f r Y F ` Y –H C h D C { ` Y W C • r f C S Q C f • W C Q è  lWCQ GjixC • pIi– [email protected] k1F y –aY ‰fQkttvghh ¦F CWF r Ž WC QQ  `  h– fCQ f f S ±fQh y tgk– ‚e…hj"w€”Ee"a¬x"€ t~UTîehh vjixC 5¨ { f r Y F ` Y –H C h D C { ` Y W C • r f C S Q C f • W C Q è  ¢wÆ t z l¨í VHz awYÝt ƒ ´“er va”¬e±Q ‚€ tg&ia“qxixC Äi1i– ë FH • W Y` C S  f C h V –h W C Q • C W F r Ž WC –QQ [email protected] TpƒF y “h í tgì– F aY ªfQktEig“h e±Q taF ë [email protected] f { f r Y `  h– fCQ f C S { f –H C f˜”Ee’aY [email protected] tf eTQ EjC y [email protected] wXeitgPiƒpjpW e—q ‡‡¡ h D C { ` W C • r C S f C Q C h S – f Yh Q FH C C S $ † ...
View Full Document

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.

Ask a homework question - tutors are online