aharonov
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aharonov

Course Number: MATH 158, Fall 2009

College/University: Sanford-Brown Institute

Word Count: 63950

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Coursehero >> Arizona >> Sanford-Brown Institute >> MATH 158

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Rc@w) c p g i d g ) y u s y u g g v g g s s A d u s C u y i A A A d u s C u s y A T& y u s y c v i u i p i g i d d u s v C u p g s v p i y x g RqqRc3@R7hchB qhR# T& P y u s y v F@hDgC Bsr (@8@00 5Th(vc@2(BTcR(|(z %r 7h#V) % A u A 8 8 x 2 0 xe u s y ) n ' & $ u v p i y x g irx#sucgEi3uqii!dRcs g6g 3i(jHsRctR 6 @w) i p g u v d u s i s s v C u s y v 3 G Rd G a (B(U G " cR%VR 6w @w) p g v i s s v C u s y i p y q4 s d u i i v S i v u g s x x d u s S p g i g S s g p !r7% rTr7 BRccRVhr77QhcrTR@T|qr7q g u g y d g p u u v p i i v p g @3 (hV i i A g u p i @cRhqw) c x ' l o ~ ln t y ' l m W l { l @(QB|@thB|n & t { t ' ~ W u p s i x x s g g v F D % g A u s A 8 8 8 0 5 x v 2 2 2 0 xe u s y ) n ' z& 9@3fh7%c(c(q@3hC Bcr (@@90 6Thc1BTcR1|q(r %r 7w@BD $ u F 4 p i % g i d g s @3r% crT3hchqi T& #$#RcrQRcs u g i p p g p g p p y u s y v H i u s g d u %(E !(7c%hqrcV) p g v j u s v u s p i d s c 4 G s u g C g p g d u s u g i p p g p g p p i y u s y cRcRTcRcQrThc3chq(TcR& H i u s g d u $rQs v 2 4 d 2 4 nn @9@BB V(6Tt C { x o k v S p i g i !(E 7R%hqrcV) p g v j u s v u s p i d s v 2 6@3 e 2 r { x o k v 8 i i d g C u i p p g e p g p p 3E(V3h@q% @7T3hchhchi y u s y ) d g g v (TcR@@!1cRQRchqrcV) p g d u s u s p i d s F D v ~ U n s z y l v m l x ' l o ~ l y s { l z y x U X v r u t s r on on m l l ' @3h#VT||(th(}|Rwt@R!tr@%r%hcfwk u v u g s y x g ) d u s u g s u y g 76crTh# QcrTr%V) rT rw) !% (TcR& ch qrRc% rw) t w s s A y u s y v u g p i d C d u s i i v P u s p y u v S 8 i x g 7(Tr@qr# ) i x S g g p x s u i p i x 8 i i g 5 S x s p C g x S p Q(Thtchqhq(@qQVcch FhDgC ABsr (8@@0 Th(v G @cc1BT(|(z %r % u A 8 8 0 5 x G 2 2 0 xe u s y ) n ' & $ ucgrTsruy%gV)dRucs%uqi rcRuchuj (TcsRy& !fc% %"r) #Qt w i C s y u v s u s d u s i % i v P u s p y v d v F 4D @@@cRq@B(" a '!r(r R7@hcVi v i i s C v C u p g s p i i i u s g u i s d i g v d p s s p qREtVRV#h w c 2 TfcB y u s y ) p g 4 4 F D 2 v @he G V@h6! BE7(rThR# V) t { x o k u v u g s y x g T& crTh(qrq#Qh w 4 y u s y s u g s p g x i i g v d p s s p v U v ~ U W { y n { x U t n s z y l v m l x ' l o ~ l y s { l z y x U u t ' { W on on m @3@VhT#B3t(tR(thq(}|R7@hhr@ r%hl { l ' k |qcfw rc 6ctcB (Trhcr tRrch#(TcR3!qts h w 4 i g p u g p g p g C s g u S g e y u s y & s 8 j u v p i S g P d u d p s s p n ' z& 1|q(r %r $ u 7 rcrT77cV$RTcB i g p u g g ) i p g F D % g A u s A 8 8 8 0 5 x v 2 2 2 0 xe u s y hC Br (@@0 Th(@cc1BT) p g C (Trhcr0 T& cq!(#h w @4 y u s y v x x s g d u s p i S g P v d p s s p C F D % g A u s A 8 8 8 0 5 x v 4 2 2 0 xe u s y ) n ' & @hC Br (@@0 Th@@c@(BTcR(|(z Ir 7hrhc $ u S p s C u u p i i u u g s y x g R77# h!7crTh#V) T& 3(RTcr# 'h 7E c (hh r!@(H y u s y g d i i x i u g p i x A v u u s y A v i u g d g A v p s A j S S u i i p d u y g s i v i y ) u i C u i p i u C u y v d u y g p i i g S p s x i g g g p x p i g u Bhc #rTqcB RrhhtR7Th qh7%7T((c1wqcrTrhcRVT6@qRTR @ A i A i A S v u g s u y g p g Rh6 % !6rTr% c e cf9@ u g i p p g p g p p i y u s y & ) g i s s crThchq(TcR$r7q% rh 'qf d u s p i j y u s y (TcR& G G b 3@((TrhcrtR7hchB RcQrThR# { x o k l X v p g C s C u p g s p g d u s u g s y x g G (((V(6! v { x o k v s g H d u s p i j #h Rcqf 2 u i u j 7qhh(7f S g d g Tc@RcQqh# d u s u i g v v { y on ' l u r { ' sn s 'n #rB@ }h|cR1U @1VERcR y l t d u s v v 4 d @ G (B(B(EhRB|@@(1`qRU who RrhqqfwhthRcs v U ' n s z y l v m l { ln t s l l y s { l z y x W n on m l l ' k v s s g y p s y i cr77q (TcRR773t cB 7qVcB 3@rTqd E RTc@Rcs cR3 !) hf y u s y ) p s i u d i p g i i p g i p y d i g p x u g i v s u s d u P u s g i v p p y e u s y ) n ' & T(|(z Ir $ u v y u 7(%7 i C u d u p g RT7@R7$cB Trhr p g C F D % g A u s A 8 8 8 0 05 x v 4 2 2 0 3hC Bcr (@@976Th3cc1x y u s y & (TcR0 q!Rchf @ v p i S g P d u s ) p p y y sn t s l ' m l |(Rwtq19fv uc @1IR@q@3hq(% 9(hq (!(hv g d u g A g A A g p v F D v p i i i v ' o l t ' o l k6W ornthqqfw7 rq7w) Rc h!`(TcR& 7rf ~ m l { l ' k u v y p d u s i s y u s y v g u i u e " 3cf9 a (B(rThR (TcR& 7rf @ U v u g s y x g y u s y v g u i u @ 2 e 2 99Q 6V3V6crThR# Tcch q%c!"hrBV 7rf r { x o k v u g s y x g y u s y ) p g s p i % u y i p s i s C e g i g v g u i u 4 d F D v i 3fq@Bh !("r% !wrTr% ) # qrf G S v i i j S u g s u y g v i U X r Y v x y g p C i u u %@(cchrg B(cTqrh'T1 rThRVrq@#c @crf @ p g u s p p i p y g i g u g s y x g ) u i j v i p g g d u s u g s y u s y ) u S s p i % u (TcR7Tr7h q# q@RcRqV #hh Rq!f v p i j d u s g u i p s v y i 2 v G d v A g G 9@(@! v che G #'(l l(Uw xlVVhrThR` TE rcrT7h rc%Qh Qs hh Rq!f l ' k u v u g s y x g y u s y ) S i g p x g u g y g d x s v s g H d u y i 2 v 2 6he G a @1l (@hE1 hcVhRwrThR# T(#Qhh Rq!f c l U x l l ' k u v p g i i u s u g s y x g y u s y & v y i v e " " 699#!@(l ((@cfwk l U x l l ' u v p i y x g y u s y ) s p i % u y i d u s i x u p x C u p y g e p y ) i v S p g i y u s y |qhRw(TcRch q#RTERcr7q7hR7hh@w$T6Tw(TcR& #hh Rq!f c v y i on ' s l on m { l ' k v u g s g y p s y i r(rhl |qcfw%6chthRr77) y u s y (TcR& h q# s p i % u !@(l (hE|6rThR# l U l ' k u v u g s y x g v e @6hc( l z l o { ' l qf&$ v ln tn s z y l v t { { x o B|@BR((9qk c v s u s % c e A x x F D v 2 n @f9966w3h# Bc 37rThchq Thqthq1@j { x o k u u g i p p g p g p p i y u s y ) s u i p i x 8 v g g p s g d u s Q@c@ERc !Q(#P g i % s P d u s v i p y v i s s v j u v i p v s Qq4 %t V77!(E$rh(% # cV) v S p g A v 3 G 4 G rv (o h(B(h@@!@B@h d 5 4 U n m l { U m l t r n t $ l ' k g i s P d u s v (q% V S s v A S p g (c ##cV) F d u s C u j i i v u g g v i y u i S 8 i x g D l 3#Rcr6chh hTrTh( hh!@Qqr# ) B|n & tn s z y l v t { { x o k l z l o { ' l R((Bfqf&$ rn ' r%hhE7R7TR# TB r@cR%r7T 3s o on m l l ' k u v C u y x g y u s y ) p g C d s p s x i i S s u i p i x 8 i u s 5 S x g g p i x i u s u g i p i u C s |7hqthq(@VhT3(T 3h !rTRc rqRV 6qRc@V $#(c #tcV) p s i y v g i % s P d u s v S s v S p g c 4 2 v i p x g 3 Q F hh!hhRq!!B G @c4 G 6(Trhcrr7qh!B 9h"hTr7chx i S g x S p p g d v p g C s d y j d i d u i 8 i p g v i S s p p g 4 4 d cB@ G % 'c cc|#rB@ BcB|Rcf|(h%!h"V) h qhq6 %fqt cV) G v g p g 2 2 d x xD v { y on ' l u r ln ln s l 'n W v i % d u s u g p i i v g u i p g p g x i p s i i v C u p g s (qh R7hch3B 4 v 4 ) ' y u s y ) u y i y (TcRt7@|h( c Tqrh'ht@Tr# q(cV) p g u s p p i p y g i s 8 g p x x s u v p i x x g F D p g i i v i p x S i v { t o X y sn t s v d y g u s g e u i g A hQhc!R r7qBRq}|(RwBhRcRchqV) !) % C Bcr (@@976Th3cc1BTcR(|(z %r g A u s A 8 8 8 0 05 x v 2 2 0 xe u s y ) n ' & $ u g s u y g ) i d u s u i i C u s u rTr% RTRcqt"rcRchj y u s y & v (TcR' F @hD u v u g u y y d g p 76crTR @@%qR|tRT QTr@qr#V) p i u u i g S 8 i x g x x s g d u cRcs hqr u i i v s u s % v i i !c%Q% rw) c 2 C v S x s p C g x S p y u s y chq(TcR& @ qh@(c p i y s u s G b #!6# hcV) e 4 A S A x i ug u s C p g v p i y v p i S v c#qRTR qE r (6 i d v H i C y P e h y u s y & e H d u g s d u (TcR`@tcs h@c i g p s P y C y h(cR c@!Qct rc @VR7TR# S s d g g A S i p s C u p g s i p d 5 C u y x g @ v d v nn @V9B VV h# 7qh Tc@7qhh(7 crTq!VB33rc { x o k v g s g p s x u i g S g d g u i u j g u g s p i u i v s A i j S i C s P 4 n ' z& 1|q(r %r $ u v u s d i 76cr@t i C u s RTR7TtTh i cB p g F D % g A u s A 8 8 8 0 5 x v 4 2 2 0 xe u s y hC Br (@@0 Th(@@c1BT) p g C s s u s i (Trhcrcrht y u s y ) s (TcRh B t Q G v p i % g p v 4 d 2 4 @3w@@@@@v G B V n u s p i y x g c% qhR# T& t Q y u s y v p i % g p F D % g A u s A 8 8 8 0 05 x @3hC Bcr (@@976Thv G c1x 4 2 0 p g B hcV3t| t Q p g i i s p v p i % g p { x o k u S p i y ) i C u s S i s s s d i C p s S p s p p s p s i 37qr7T$! h htrr7hcTrhch e u s y ) n ' & T(|(z Ir $ u v 7 TrhrcQrcR p g C s s u s i v d v ~ U n s z y l v m l x ' l o ~ l y s { l z y x U X v r u t s r o on m l l ' k p s i 6!f||(htq1|RwtR!trn p r%hhEhch i s s s d p g hRch%B TrhrVrht ThB q() cR7crhcRT@Qc G G p g C s s u s i y u s y ) s 5 p i x s x e g s u C p g i d u s e v A i A i A S h3 % !V(hhh!7r3cB R7h 7#(7qR rcRht (TcR& t$Q v s S s s u i d i i u s p g C u p s i u x i u s i y u s y v p i % g p 2 u u g s y x g 7crTh# y u s y ) p g (TcRc c Tqrhc rT rq# @E7w!) p g u s p p i p y g s s i y A A y u s y ) s (TcRhB G G cc G @c BB V(k d A x x v v nn { x o d u s p A t(T7h! % A 2 F i p d p g v i d s p i i y D v d i v g s s v { ' s on m l { ln z l t x ' l on y sn t s cfe G Vh!Rr# 'qV7!BREhB %3q|r!hRB|6f(#1qr|( y ' l on 2 uu u v i p g i i hr{ |7@ T B7qV (7!t R777q4 Rc RhcE !q(@Q d u g S i C u g p i C u i d u s i u p g P v p i C p i u i i p 2 F D u p x i p x v H i p @h7h(77@T Rc%%(Q77T!% Qct hh!Q @ d u s i d s s v H u j v u s i g 2 G I(V(76crTh#3 d v r { x o k u v u g s y x g v d u y g C u s (c(7P y u s y ) u s p i g e y s (TcR%cqrhhTrB cRT g S p g i u s Qct hh!Q i g 2 y u s y ) i C u s p y s (TcRT%R7TTh @7T3hchhchi i d g C u i p p g e p g p p Tt3h B7T y u s y ) i u s u g i pe u x e v 9( % R! A i A S y u s y ) g (TcR rw) ct hh!Q @ s u s i g 2 RcR@ C u s y ) d u s v G cc G @9(B(6crTh#3 d 2 5 v U v u g s y x g e 4 v v i p cfcc( "hrT q# ch37h(qr77 Rc%Vq qwRcfqR4 hr@i S p i % u u g i u p v p i d u s i i p i p i d u s d u s i p y S d i d { l y { l v t y sn t s t(w|( q| 7t rhc3TcrT!Tr77chR#V) rT!#Rch@q!% G n u i p g i s S d u s S s y x g i p s P A d u s g p i A 2 A i x i i 0 d y s 0 s u g 0 y d A u u i x A u g p s A i p y y 0 5 x 5 u d u y g i u s tu y t m t t ' t # |# hqRc!1TRc (@i q(y 6chVi T| 0 Th7c (cB7|w@@f{ tu g i p y r Tr7RcrcV 7#B7|@@hr7hqh #t ( th VB! Rc! @ A u s x v s u g i p s u tu y t m t t ' t { tu u d i u i i p x i x g p g i i g A d y s A 2 y 7w A @ d i u i p i 4 2 rqB qRT q!Q v p g i i c6(hc! v S u s x g ) d u s u s i i p # VEt RT7hr77hT|ERc% qhR#V) ch(c !Q S d i y x v S s s p u d u s p i y x g v u g u g H d u s S i p s 2 v u p i v C s p i e p i C u p x v i g 677hqV rhqwhhq7h(h! T& ) qR7!Q y u s y v p i u d p s 2 2 A S s p p s C u i p p g i s u g u i d i u g v s A hcR7Thc3 qh'cRcrT(qt@%Rc" !f s s p s x i p A A h V 5chr@ rhqh cfcc cfcc hch R7T# ) 7# Rc% ! rhqh 7@c% B7r 1 p g d i i p i v 4 e 4 v 4 e 2 4 i C s x v p s i i C u y x g u i u s d i p i u v g v s A S d i d i v v ln tn s z y l v t { { y l t u v S s p p 3hr3 @BR(((#@1V7@!h cRcrT(qt#VR7ThcV) q@" !f s u g u i g i g C u i p p g i v s A v u p x i p x v p i y x g d i @37hqh# rqR y u s y ) i d u s (TcR#RTRc!V(r6 E 0 v C g v u s t @ d i i p G f a !c3V(|6rcr#Tc% h ) @3 e A S A p g i g A H A u v C g i % s p i u g g g g g d u s j u d i p 7c(Q7@@ v i u i p i y x g rqh qh# ) c@R@6hrT q# ! g g g v S p i % u y s i v G h9c(qrhQcrTh# (TcRc%(crThr# hr@qr#V(( qRcQ RTc @ 2 2 e p g x i p s u i g u g s y x g y u s y ) u g u g s S 8 i x g ) v H p i C g d u s i g u p g x e g s i i v "rThch G h@ e 2 b v 4 e 4 @6h9@ a 3(@B(h1 qh# QTrV! rT!7Tr%Qct( G { x o k ' l o ~ Y n W u v p i y x g i S x C u s y u s u S i { x o k ml s l u v pi y x 3!h@1(1 qh# A 2 e v S p s y p i i i h6@QcRhqR'! g s u s i crcRht (TcR& fct( y u s y v u s u S i 4 C A v 2 3@Rd G @r5 G q(B( chr%T 2 v U v p g s y Th q# Q@cr( y u s y ) s p i % u v d S g 4 2 4 G b v U A i g p x i i x g e v A p x 3( @@c9c a q1991 rcIhr# h#chh !R7T # (H v 4 d 4 i % g g C u v v C s p i e p i C u p x v S p g i g C u d g @rhqwhhq7h(VR7@V) u s u g i p p g p g p p c3crT3hcchqi v 6 u g x Qh7( P H u u s 7c% u s y ) i d u i !i g i p y rgTRi Bq!r77ych(7uV%T q! i A i C s x v 4 i y g v i A i A t3t(7c% % R(H v G @(v b I(7 @qhh(hr d v v r { x o k u i d g p i i g d s i (TcR#ht@ t%h%t V w) qhrtRq6 G y u s y ) i s 8 g p x x v g y s s d u s C u s y v u i i v C u y i 2 2 e v h@(( a BhRc(! %!) "@%t hthVh t y g A i s u s p A d s A A v i d g i d i x p g g u y i A i p i r7T % ! i 7hVV R7h G 3 q6 G p C u p y g i d i u s p i i @ERcRv G ("!"( t3 2 d u s A % i A i A H p i y s d u s qRc6 G G A v @c G 9 G 5 G G @(l h(@RhVrEh !"rht d v l m l l U x l { t ' ~ u o k y i y u s i A S v i d g C u i p p g p g p p !@R7Thchqi S u i ue C i i TT qh7Bcr!t y s { l z y x U u t r o |R@(!#rn y u s y ) i p i (TcRV qt P T V%qRc6 y u s y ) A p i y s d u s i p y qR4 2 e v A i A i h3Rh6 % d u s !!) qRr %%tR 6 4 G H s v i y ) v i s s 4 G h9 G RRh6 % !% 7cRchcRchTRcrT3rhcrc1 %ch 4 e G 4 v A i A i A S p s x u g g x d i C u s u i e u g s p s g x g i p y g G d u s 7QRc @qrqR$qR777q4 #qh| 7qQtrTh(#rV% G g u i C p i v p i C u i v P p i p y u i v i s v s i F 3wV) D (B(!BR(thB|@@((l e v U ' n s z y l v m l { ln t s l y u s y (TcR& VV(VTe w(cTtRc % G g p i i g x i u H y g p s d u s s d u g F D % g A u s A 8 8 8 0 5 x @hC Br (@@0 Th d u s i s w"hV chtchr$7w cB77! G p g p p j S p s u # S p s u e u g v u A j s s g y ththR hh@%hr7 i s i u %r $ u v i d g 7@ @V) v 4 2 2 0 xe u s y ) n ' & c1T(|(z y u s y (TcR& F D @h% C Bcr (@@976Thc@@@c1T(|(z Ir 7! rT"T g A u s A 8 8 8 0 05 x v 2 2 0 x e u s y ) n ' & $ u d g i p d u s i d g p g p p i 5 u g s y x g Rcq@tchrThR y u s y ) u i i (TcRqr77T"@P i p y q4 RcEt 't77!2 G d u s i s s v j u e 2 2 A % i A S v i d g C u i p p g e p g p p i y u s y ) g S p g i T!"! @3t7T3hchhhq(TcRtcRT @3tR 6$677!c i s s d u s j u A v A x v g % v U v u g s y x g 34 G @cc(B(w6crTh# v 2 2 0 xe u s y ) n ' z& @c1T%(q(r9 %r $ u v i d g 7 @ y u s y ) u i i v i p y (TcR%qr77T fqR T) y u s y 4 dusv i ss Rc%tR6 v j u 77!c F D % g A u s A 8 8 8 0 5 x @hC Br (@@0 Th d i s u i s u g 3hRqhRcV) %t Rc`77! v i s s d u s j u u g s u y g i s % p x v % i s A y A crTr%3#hch"hr!6 e u s y ) n ' z& Tt(q(r9 Ir $ u v u g S u s S u g s y x g 7(cccrThR# c F D % g A u s A 8 8 8 0 05 x v 2 2 0 @3hC Bcr (@@976Th@@ccc1x y u s y ) u s p i g e y s (TcRcqrhhTr w y % hr! i s A v p g i i v i p @@3(hV @qr(Rq3 Rc% rch7 @|(tfqf#(t y u i v d v i % s ) d u s g i g P v s g p P 5 d i vn y ' s { t X n s z y l v ln t s y y l v y sn t s v i s C i p i x i u g i p p g p g p p i y u s y ||((@B# |(Rw h q(#%TrVrThc3ch(TcR& w#% hr!c y A A i s 4 e u s y ) n ' z& T(q(r9 Ir $ u v i g p x p i s 7"rqr7chh F D % g A u s A 8 8 8 0 05 x v 2 0 @3hC Bcr (@@976Th@c1x u s i r7q( RTRc% t Tt T& 6w % hr! G i d u s u i i p y s i y u s y v y i s 4 e v c9q3( 5 a y u s y v y (TcR& E % hr! i s v { x ' U n t X t { { s u v u g i p p g q(o @f%BqV7(crT3hcV) chtRc(Trhcr(crTh#V) p g p p j d u s p g C 5 u g s y x g 2 v v c@3c1 b i u i rq i S i % a { { x o z m l { ln t s l S y H 4 d v A g 3r@cc(! Ra BRwhB|@@(( A i s y ) i u i g C i u i u i d u g x i p p g rTr73|V B7qV( rRT7VRqRc1T hcV) crT rw(TcR& 1$chq7T'$$ cR! s s ) 0 y u s y v u g i p g d u s u s & s l m n { s { { 'n y l o QRq|!B|tB F i p "hrT q# cB!h6 v r6BcEhRq(B3!hB|@@ S p i % u d p g 8 e D v d i u t n i C C y P v { m l { ln t u C u p s i x x s v u g s y x g 7R7hc16crTh#3 (TcR%qt rht th y u s y ) d u s u i i C u s u j s g H p s u i v y p s ht(q!(@hc (qh( g y i y F @hD i u i i u d i u i i p x v F 2 D p i S s u s s u i p i d v u % i d p g 3qrQRT7hqh Vq@@hq@rtrTqq(7@7%c6 c 2 G c%@h((@7qhRV) T& h #rT3 rqR e 4 F D 2 { x o k y o v Y u v p i y x g y u s y i u s u g i i u C s p s i y s u cg r hh Rq!Qh (Trhcr T& %rThq r 3h E Rc RcH i g p y i i % g g p g C y u s y s g u g s u i i x v s g A d u s i u g A H A (# hcthRc64 G c4 G @hD G G h@7h#V0(TcR& RcRch rTRc rqR g s i i d u s v e 4 F ' sn t $ u v p i y x g ) y u s y i u s u g i i u C s p s i y s u g c` Trhr hc3 T rThq r h !6#%3h E "( p g C p s i y u s y & s g u g s u i i x v u i u s P A P A d u s s g A v i u g H A H A C A v i p c6 r# 3! G q@(6q|rq{ i d s v e A x x v {nu s & n t { ln ' $ xn u z y l v t { y on ' l u r 9w(q1%B|h|39I1 |B) r(Q(%rBq@ ! Trhr |Th77cRc(#e 7c p g C s g p v u s 4 u v i S s P e 7"hh!h'7cT T7crThR#w(TcR& y u s y ) u u g s y x g y u s y @ 4 e 4 F D %@h G R%(B k v r nn { x o i u i d u s qh q% ERcV qRc(#ct!h G p i u C s v u s % p p i x A A g d u s v y i x g A qr771%RcRqh"(cR1 v g A A P S d i d i v ln tn s z y l v y sn t s the hr@B|@B(|(Rw n B|cRh|(h7c(chRq@hC Br (@@0 Th l ln s l 'n W u p s i x x s g v F D % g A u s A 8 8 8 0 5 x Ir v 4 2 0 xe u s y ) n ' z& @@c1TE1|q(r $ u v u g s y x g 7 rThR# y u s y (TcR) cqrh r @ u s p i g y s H i p 77@T @ F i p d p g v i p 3! "r# qV7!BVrt#1|6f(qrn i d s p i i y D { l on y t {n z l 1 x ' l o y sn t s |(Rw G } "q i p i c G c G Rh6 % !(Bq@t !& Tr'R7TR# T) e A i A i A S v i d g j S % s 5 C u y x g y u s y d u s v u g s p i g y g y u u g v i u i p i g i RcrT% qh(ct(cR@7Tc3wq@ qr714 Rct7w) # 7@c!6%hc3r77q p i g d u s H s p v p i u d p s v g p s i 2 F D % g A u s A 8 8 8 0 05 x v 2 0 xe u s y ) n ' & @3hC Bcr (@@976Thc@@(BTcR(|(z Ir 7((hr#s $ u v 8 g s rTr73hqhr(T c3! qhR T& rq!(Vqhc3!TE7thc@Qc g u g s x x s d i s p i x y d i i x g u u s p i y x g y u s y v % g C e A 5 8 i u g u g s i i u g s u y g rTr% y u s y ) 5 i y s i x 4 g u v A x e A d g (TcRVT rq(3 R((@ (c A H 4 v S i i e u g d d rT Qhh! Tr@qr#V) cRcrTh#V(#) v S 8 i x g s u g s y x g ) v P A g A S g A g p v u g s x d d u s p i y x g @R@@(|T7T @V qhR} T& q y u s y p i j 4 e cf9c !QqR7# E e u i u g y v ygrhTr# p d s x s a 1 ( A d u g s s ttc 4 c G G h % @!!chVh(TcR%rt c!@Q @w$Rc e v A i A i A S v S s p p s i s C y u s y ) i s s p C g p C u s y ) d u s o rn u i i qhqr ' p v ~ U n s z y l v m l x ' l o ~ l y s { l z y x U X v r u t s 3#VT||(th(}|Rwt@R!r n m l l ' k v s g u S g x s i p s o %hhwcr# r( % rTR|c3rc@V ##RT1E @QQchc u g u y u s i g g g i i p C i d i u e v S d i C i d u s u s 4 | cc!rcr7VT RTh RTtRcrcrTh77@6ct(q!c% g p u s C p g i s i p g i u S i d u s C g s g p v u u s y i u g v u i u g x g i s i p u qRc(%rcr7qy v { x on ' t v X l t o U { sn { tn t y ln s t u cT%r3@| (9B|3IB@B7 u g s u y g i s % p x v i s y rTrI hh#qt G F G 3h(6ch37h " D H v u g i u p v i p A % u # u g i u p v ch37hP i p y 4 d u s Rc qrqRhr@@|(tfqf#((|( 7Rcs H p i i i S d i d i vn y ' s { t X t x ' l o ~ y sn t s u d u v F D v 4 e v v l qchhcc1# @(l c(Vh7 hh % rcR3 V%RRh(V l U x l l ' k u v s p g S s e g u s i i % s i i g v g A A A v 4 e 4 5 nn @@9T@@4 v B 6h#rr T) { x o k v i s C C g y u s y s p i % u y s g u g s p u g i A H d u s i u d u s ch q# crTTh(c !(RcrqR7Rc` g u s v j h6 R7!E R@q !) @ c C u v g i i v i g p u g 2 A % i A S v p g p p i p d i s x i u g s y x g "6!( chqB hhRQTrVcrTh#3 T$ y u s y & % !!h#3 A i A S p i y x g y u s y ) i % s x d s u (TcRtT7T @tf7 P G f9@c e 2 C u p g s g s p i R7hch333q!) qRr d u s H s v i y ) 4 i p y Qq4 4 c G q@@ G Rh e Ai d u s RcfI!'r H s v ) i y ) F S i i e u g d d rT Qhh! D P i p y Qq4 i G 66whh%c% |Br(h9(B(#rBR|(%R|B|RhW 1 B(1B|@tm d A x g xn ) u z y l v m l { U on { sn U n snn { tn t U ln t y ' l & W m l { { x o k n t x z l 'n xn ) u z y l v u v u g s y x g hth9qo 1(qh|(V r(}7w6crTh#V) T& qr7cQ3 (7c y u s y i s p s 2 y g C p s 4 Tchthq(@q77@@th(q! y u s y ) s u i p i x 8 i u C u d g i u i A 4 e 4 c@hccRv b (h3 "R!66crT3rI A i A % i A S v u g s u y g p i C u i 977714 Rc%rV%(tqh| 7qQttrTh @ d u s s i v P p i p y u i v i s 4 v i u i p i i jD v { l n ' ' l ' l ' ' m l x ' l n o ~ H i u s g d u s Rqrq@fqr% hBw@q||chfqho (@3rQH A x x v v v r { x o k u v g 6r IR3E7@ TTrVQcrTh# ) y u s y & i u g s y x g T& y u s y F hh s d p i s s 777 4 v e 2 3c RqR7rRcV 6 @ g u i u d u s g 4 4 4 G 4 e G 3 "R!(BcR ThcR# Trq%Vt@Q@cr( A % i A S v i u u s y u s y ) S g u s g S s x s i g d S g 4 G c4 G Rh3 "R!Bch qV!hrcr e v A i A % i A S v s p i % u y i s C C g y u s y ) S u s g d S g (TcRch t@Q@cr( b a i u i g s i i Rqrq@Eh3h b i u i v p i y x g a rqqh# y u s y ) i s s i p S s u i g (TcRrh7cr7crTqh(x A F 4 D q@h G E@cr( @ d S g 4 (C 4 4 e h9 G F p i C u p x D v d i v H u i i y i i 3q7hh (%qVq3 c% Rc`q@@VBc@3qrqhR#V) 7 hwT6!(7) u s d u s H p i s i d v 4 A g v i u i p i y x g u i g i p y i v y y e g g r7cV) Tq"|#fqfw(Rt B@tBR!77TRQr7T % E7c( u i % i v y y t ' l ' k t { t s tn t y ln s r u v C u y x g i p i i 2 g g g g F D h G R7%(37 htr7@cRT%c #(crTrqhc3T T) v v r { x o k u v p i i g 2 u s i p g p i % g u g s i p p g e y u s y crTTh t %chthq(@7TR7 #q%67T!BRqw (wBqhhrV @ g u g s p u g i d s u i p i x 8 j u A v u i d u A P v C g p i P A g v u A v i d u i p A H v i g A 4 A 2 v u i d p g v u s d u s u A H A d i i u i p i g R Tqrq@QrhcQ(RcR (( RqqRc3 (TcR! y u s y & u 7 q 7% qR7ThRQ3qB qh7VR7TRq! q@3hE G 4 G } "! u i u g p u i C u s i p s s S i u i p i p i u g C u s x i d u s A F 2 D v A % i A S i p y x s p i u i C s 5 i u i p i p i u g TrcqRq%Rqq qh7V % rRcQT7chthRt# Rc}cR # hqh@Q g d u s S u s p i u y i s v S p d u s % g u g p s v u p i 4 4 4 4 F @he G @hD u v C u y x g 7R7T#3 TErcr7tcB q 73hs y u s y ) i s i p p g u i i p y ) i p i g u d u 4 3fhe G @ b A S A x x (!(B h @rTt B 7 v p g i g p x u g s p g u 7qr7cVtTV3R i s p s x v i v i s x b { x o k o {n ' l @333( i u s i Rch@Q G Rch@Q @ i u s i TfcTQr!Vw y u s y ) x s p u g i g v @6 eRRh % R!(T RTh hhh (TcRRc(6crTh# T6rTr77chh T! v A i A i A S v i u S i s y u s y ) d u s v u g s y x g y u s y ) v u g s s i % F g A u s A 8 8 8 0 05 x v 2 2 0 xe u s y ) n ' & % C Bcr (@@976Th@c1BT(|(z Ir 77hq|c3Vh |@(cwhthhr# $ u u p x i p xD S p g i g A u A u s p g j j j g d i e y v i d g p i y e d i i y u s y v v 4 e 4 4 v A i A S v i d g C u i p p g e p g p p i T @3qr7@ (TcR& (hq@!% !@ @7T3hchhhq T) y u s y i x v v r#3cfe G cQ(h6 % (!6T TQ7! @7T3hcch(E Rch@Q A i A i A S v S p g i y u s y ) u i d g C u i p p g p g p p j v i u s i A v e 5 4 v @fq @Ir l @(l h(VcfwV6crT3hchqw TQRcRqqB qh7trqrTr7Tr Rch@Q m l l U x l l ' k v u g i p p g p g p p i y u s y ) d u s i u i p i p i u i p s x i x y v i u s i 2 v u p x i p x v g s 7hq@) w) # crc e A d u s S s % g g A u g s u y g i s % p x v u g 6crTr%hh}QctQc p i g q1ch!e v G Rcc@6v Ra v 6!@`Ih6crThR# T%qc1#TQQ3 ctQ 4 d 4 4 x x v A g b z y l v Y X r W U v u g s y x g y u s y ) g p i i g x i u e 4 u g v 2 e v ~ U @3cf9!Vf n s z y l v m l x ' l o ~ l y s { l z y x U X v r u t s r ||(#hq( |qRtRo n q r!hhE7@ q1I(@Ir7T3B$ctQc on m l l ' k u v p i y u i s i u e H u g C u d g s s p g R7@@crT rqB rTrTqr!7773 RTrcRcs i u i d s s i g C g s u y u s y (TcR& @3 2 e 2 2 A i A % i A S v S p g i 3(h3 "R!Rc3T i s s %R 6 Rcs Q d u p g A 2 2 0 cc1x e u s y ) A i p x j j j A v s u p g s T% "wB6rhcB 7) hr# r @c 9(B(%B(hB|@@(( v g s g v d i C s x v U ' n s z y l v m l { ln t s l on l y s { l z y x U n on m l { l ' k u v u g s y x g rw|qRo Rrh|qhIrThR# Tqrchrc }Qc y u s y ) u s p i g y s v p g 4 5 v r { x o k v S p g i @I3%ct"t p i y x g qhR# y u s y ) u i u i p i g i d C u y d i p p g (TcR7RqqRc37@cB A v 4 @fe G c 4 i i v t Rh}Q G p g p i g e v 2 d 4 4 x x v A g b @q(ch3!6RcRv a v 6@wIhRqhR z y l v Y X r W U v p i y x g T%c(Trhcrh3qhrTrhh hB Trhr%t Th7r#RrcRQVQ y u s y ) s u g p s C g i i p d d u s u g s p g s i p x p g p g C s i e s g u S g v p g A G cc e { ' nn qBB |qcfwB|@thQ7(qh@%rT Trh h1|r|#f7 (I(7hh c 7# Qc { { l ' k ln t y ' l m W u v x i i p F F uD C gD e u p i y C u p g s p s 2 % i S "!rThc3chq7T 3@%hd u g i p p g p g p p i d u s C u i g p x s s T& y u s y G 6#h G A x g s a (6hh!@7q A H A i g A S i u g s u y g g S p g i s s i s rTr% RTcrTt RTt 4 j ) u g u u s cRQ 3 Ir $ u i i d u qhqrRcs v ccR qRt(@@Q p i s y v F D % g A u s A 8 8 8 0 5 x v 2 2 4 2 0 xe u s y ) n ' & q@3hC Bcr (@@90 6Thc1T(|(z u u s p s A 7c7# T& y u s y d u s u s y A H A Rcct@h1( 4 v S i i u g d d 3rT QQch@ 6crTr@h" rcRh A u g d i d i % i p v u s i u p i d g h@ c@7(H ( @ s p y ) s A A H e g 0 @f) Q (qc3r3(Rqrq@%h#V) c chc( 0 g v p g x i s u i g v i u i p i y x g p g S p g s p g s g Q hh!h h@Bqr7Rc% TRcrT hrcr@ct r@! Rc 7# (%!h"V v i S g x S p S i e y x d u s i p y s u C s C d u e u s i d d u s p s v i % A i A i A S v i d g y u s y ) i % d d s u g u v h3 % !(@(TcRTrQ(# tRcrs H i u s g d u 4 @@d G tc %(7!%(7c @ p g v P u d p s P v j u s C #C e g e v F 2 D 4 4 S s d g g S s s g ch!1q@ht@! rT!c3rT rqth 2 2 0 xe u s y ) n ' z& c@(BTcR1|q(r %r $ y u s y ) (TcR |crTrT(cT!RTRc%RqqRc3!#P g p u g u s p i d u s i u i p i g i v p g C s C u p s i (Trhcr7hch A 4 4 d @ G 6q( v p i i p y 4 q @c 2 u v s x g 7%BcT F D % g A u s A 8 8 8 0 5 x @hC Br (@@0 Th y u s y ) p i % g p v (TcR q!) 7c c s s 4 2 4 F D h% C Bcr (@@976Thc@2 G c1T(|(z Ir 7 7@Ir g A u s A 8 8 8 0 05 x v 2 0 xe u s y ) n ' & $ u v i p x u v l @(l h(@hI h#3 Tw"hh!h T crTr%T rq@!$7c G c m l l U x l l ' k p i y x g y u s y ) S i S y u s y ) g u g s y u i j v ) s s 4 2 ' n s z y l v m l { ln t s l R(h@@1(Ql G G 6wF G 3h@VT(B(U d A x x D v U v y s { l z y x U u t s r on u v S 8 i x g y p |RR!r@7Tr@r# rq7 T& !) w) $ @c y u s y v e g s 2 G ((hV v p g i v i! i @rR9@3(Th! hqrr7q#Qcrh (thqfI(1 |B||@rV p y u i v 4 d 4 v i p S i i p p i d u s S y A e u s p s 5 d i n y ' s { t X t xn n tu uth(B 96( |(Rw hh@(TcR& h|r7cRT 7ThtT T3 ' { n z y sn t s i s y u s y g S s y C u i g i p y s i p i g g 2 qhh@Q c 2 v a T(Rcr%(c(TcRtrcR7T }P i p y s v d i u g i g u u s y u s y ) i C u i p y 4 d u s q p i g g 2 2 qhh@Qc u g s u y g i s % p x v u g p i d C A rTrI hh(6ch qr v i p A % u "(# Ir $ u g i u p D n y ' s { t y t x ' l o ch37hB(hqtt(qrn T hh!h y u s y ) s S i S y sn t s |(Rw G R#P v d i v F H v u g i u p R(hR7h i p y 4 d u s Qq %qr H p i i i u p i y x g 7qhR# F D % g A u s A 8 8 8 0 05 x v 3hC Bcr (@@976Thc2 G (BTcR(|(z 2 0 xe u s y ) n ' & T@(Bc(crTr%T r @ y u s y ) S d g e S u s g u g s y p i u i y u s y ) s u g u i i u g u e v H y g p s (TcRcRcrT(qtRc(w TQ v (2 G c3Qq9h6#B#r(wht hcr77q d x x v F D { y n { x U ) u z y l v v s s g y s p s y i A v d 5 v U v r@(B(1 A y x g A s R#V) 6T rThRV$r Tr@r# V) V v u g s y x g ) C g s u g S 8 i x g i g v v u g s p i x g i rTq(rT TrhEchq rqcB hcVhR(TcR3 p s S p s u i i i p g p g i i u y u s y & u i p p s QqhcQ @ 6A G q6ccrTr% e A x x v u g s y u g u d u s C i v C p i 4 h 7@hrthr7crh'cq G @E % R! e 4 A i A S q@RqcV #c@ G p i j d u s g u i p s v s p d i 3v G h9 q9h@ (B(U e 5 F D 4 ' n s z y l v u t n ' l o ~ A u g y g i y ) u y C u i i d s S s i s R(qB|h((crTR7ch RrR7Th! h ! #(# c7qwQRc r7c @ A u s p s d u s u s s A 2 p i i % g 3#(I"! v 4 3 G e G 2 G qF G @ (B(VBR(6B|cfq1wB| qc17crTqRc(@!(c3crT@# r7c 5 D U ' n s z y l v u t n ' l o ~ A y p i i g x S s u i u g x 8 i i u s u g s C i v A u s s d i y x u y v u s s 2 T7r7c 4 4 v A p i A g A s (#(q@(@1T ( @hc%3h 2 G (v a #(1@1T ( A d u g A g p g s i i A p i A g A s A d u g A g p v i g p x C u y d i u u j i g u g s x x s u s i v p i @("rcTR@rqRhh RT!hQrTr7ctTrV q(% @rh# G 7h y u i s y x g u e C u p y g G hc@@Rh6 % R!6rcr (TcRcB B T hRx 4 e 2 4 A i A i A S v C g y u s y ) p g i s s u g d u g g u i i p y s i H P i d u s P y s rTrRc qt TQ#r%!T(c Rc6 () @@# & hhR @ v i C u s v H d g g P v i i p y g A v d 5 v r { x o k v p i y x g @@@9 R%(3 qhR# TQ7%RqqRcR77h7c # y u s y ) u i u i p i g C u u s u s v y p u Qh#

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Sanford-Brown Institute - MATH - 158
%!PS-Adobe-2.0 %Creator: dvipsk 5.58f Copyright 1986, 1994 Radical Eye Software %Title: correct_review.dvi %Pages: 77 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips correct_review -o %DVIPSParameters: dpi=300, comm
Sanford-Brown Institute - MATH - 158
New Directions in CryptographyInvited Paper Whitfield Diffie and Martin E. HellmanAbstract Two kinds of contemporary developments in cryptography are examined. Widening applications of teleprocessing have given rise to a need for new types of cryp
Sanford-Brown Institute - MATH - 158
Sanford-Brown Institute - MATH - 158
8BhHgVbhbebbCIS)CfIwt'eCCwvdUbIebVX4IVSshHgSabhUbvkhvhbIw#w c f iF d R U u iF P RH v iR r P w H c i q i R U P 3 PRR P iR f PFH f u d uRH R r w i 1 B f P c R `HR f d H R q i H H y B H v P H c R U HFH f i d q i FH c u U f P c tb
Sanford-Brown Institute - MATH - 158
%!PS-Adobe-2.0 %Creator: dvips(k) 5.86e Copyright 2001 Radical Eye Software %Title: hw4.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips hw4 -o %DVIPSParameters: dpi=
Sanford-Brown Institute - MATH - 158
45 6" fF f4 )' )`c)EfY!E6I3Eb6 5 6h!wrd % h I% dI" I F" Y d D C d Y 6h !6"99sw')XEC E`E 6"d 6!jErId 'EE)9u!3VwC % Y d I Y aI Y h C% I% 0I e d Y"% h " C d ( C F h d % a 0I I Y a ( iI d 5R5 6Id 6')Ev)6IX6" 6d !W)EV )w!6!
Sanford-Brown Institute - MATH - 158
2 F D6( R " % k H D" j " 06 0 D D 06 % d l)7CC!ICQCF Cig6C!)QC)h)g69$" CB'f$e D"% D 06 ( R 6 0 D % 4 4 4 06 " 7" $" C)E!CC!)C)6H 5CQxw 6( W 6"6 0" R6( 06 D 6% 0 1)7!GI!)Cs!)77AiqC)$" I'2 r yh w2c a tX R F % r ph f2c a YX " 6( W
Sanford-Brown Institute - MATH - 158
%!PS-Adobe-2.0 %Creator: dvips(k) 5.86e Copyright 2001 Radical Eye Software %Title: hw5.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips hw5 -o %DVIPSParameters: dpi=
Sanford-Brown Institute - MATH - 158
2 D"% D 06 ( R 6 0 D % 4 4 4 06 " 7" $" C)E!CC!)C)6H 5CQxw 6( W 6"6 0" R6( 06 D 6% 0 1)7!GI!)Cs!)77AiqC)$" I'2 r yh w2c a tX R F % r ph f2c a YX " 6( W 06 T R6% F H D66 H6 D 06 8 6 11x`evu!sCUqigedb`9)7!GECVUS!'17C!Q!( 'P%I7!)GF
Sanford-Brown Institute - MATH - 158
%!PS-Adobe-2.0 %Creator: dvips(k) 5.86e Copyright 2001 Radical Eye Software %Title: hw5new.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips hw5new -o %DVIPSParameters
Sanford-Brown Institute - MATH - 158
Sanford-Brown Institute - MATH - 158
Sanford-Brown Institute - MATH - 158
Sanford-Brown Institute - MATH - 158
56l T&PF& T&P&Thx!&da2e&F" yBI &!TP&WH S Q # %" Q o " H S@ H ` H @" # H H " ) H S b S b w" % bI %" 1 H ) S H S ) b S Q @ H S ~ @ 1 ~ x ) o l ~f # t&AVW91!Tq@&iH TCaTP&$ 6 9T&v9"}pPtsx$ veg}g 5 vgt | { zyx o ) b S ) E S Hw
Sanford-Brown Institute - MATH - 158
%!PS-Adobe-2.0 %Creator: dvips(k) 5.86e Copyright 2001 Radical Eye Software %Title: lasthw.dvi %Pages: 1 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips lasthw -o %DVIPSParameters
Sanford-Brown Institute - MATH - 158
Sanford-Brown Institute - MATH - 158
Sanford-Brown Institute - MATH - 158
uv7EC}7Pv 7uPeeEse&uY7 ECu 4CE3CP0#"CeYlu7eC YCu0uqdCsECbY# ee4tb}W GEPQdYGude W &5e7 9 3 9 3uduehCs ECuu 9 EYu7EBPC0C9P# d YE37E9 D " E7uuqCe
St. Josephs NY - COM - 152
Starting a New program in the JBuilder Environment(Non-GUI I/O saved on diskette) 1- Invoke the JBuilder environment 2- Create a new project: Click File-New-Project to invoke the Project Wizard In step 1 of the Project Wizard: Type the program name
St. Josephs NY - COM - 152
Chapter 9: A Second Look at Classes and ObjectsStarting Out with Java From Control Structures through Data Structures 1eby Tony Gaddis and Godfrey MugandaCopyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-WesleyChapter Topics
Bowling Green - MATH - 592
Bowling Green State University Department of Mathematics and StatisticsMath 095X Intermediate Algebra Spring 2006 Instructor: Contact Information: Office Hours: Course Coordinator: Stacie Posadny; staciep@bgnet.bgsu.edu Course Description: Some or
Bowling Green - MATH - 592
Bowling Green - MATH - 592
Quiz 1. Solve for x14 x + 3 =2. Integrate4x "8 6!" 5x4+ 3e 3x3. Find the formula for the following graph!Note that the roots are at -1, 3, 5, and f(0) = -45
Bowling Green - MATH - 592
> Ten useful applications of Maple > > 1.) Maple can expand tedious expressions > ex:= (x+y+z)^12; ex := (x + y + z) > expand (ex); x12 11 11 10 2 10 2 4 12+ 12 x y + 12 x z + 66 x y + 66 x z + 3960 x y z + 132 x y z + 660 x y z + 660 x y z 8 3 8
Washington - CHEM - 239
Penicillins - Chem239
Washington - CHEM - 239
Washing Dish with SoapChem239B, 2007At the molecular level the detergent molecules are adsorbed onto the grease,and your agitation or scrubbing is breaking the grease into small droplets.The role of the detergent is to prevent the droplets coa
Washington - CHEM - 239
Quiz #1, Chapter 19 Review Questions (Chem239B) Prof. Sasaki -(1) Write the structure of the following compound; (a) 4-Bromobutanoic acid, (b) m-Nitrobenzoic acid(2) Which of the following compounds is the most acidic? Which one is the least acidic
Washington - CHEM - 239
Chem239B Spring, 2007 Quiz #2 Prof. Sasaki _ 1. When the compound A is allowed to stand in pentane, it is converted to a constitutional isomer B. The most likely mechanism involves an intramolecular acyl substitution reaction. Draw all steps for the
Washington - CHEM - 239
Washington - CHEM - 239
Washington - CHEM - 239
Chem239B Spring, 2007 Quiz #3 Prof. Sasaki _ 1. The use of epoxides as alkylating agents for diethyl malonate provides a useful route to lactones. Write equations illustrating such a sequence for styrene oxide as the starting epoxide. Is the lactone