Top Banner
EXAM lElA) h!0WCE (D fe rt ;:= 000 (. 'X '1'+/12.) =. I ii'Zq b 8... '+3 F:. pC 1+ r-c )-::::.(Qoo( \ 1- $ N -:;'6\/),1"" 9 'fY\,(J'f) M S b) \DO"* 6;l =- ) - 200 lJYl VY\ c,) 4000 * . J -= ) 20 to )f/2 0J.At€. .L\ - ,2,0 =- 5 ) \ \- = 3Cfco J? I \"}- = 14 I b e) N;= - .. 1)-\ :. 5 <g prrrr LEF,- Pm\":.. - 00 ;V-\ R)=- 0 341L.\ 152- {JV-:. ® N::: \ d-. {)mT -= \()OQ rr--? $ aL\ <6 )330 1<1 -g 1:. -::: (p fv 0 p\J -==- PI::: \ 2- ® N-;:c ,q ?mio;. 0 -;. ? J'{ '= I ® N-=- \ ?t'Y\T::.3coo I == l1 -)l c.p.\) \\\\ 'J...1 1 0.9. $.L\23'5, \ VVI -90=0 :;L It4-h I.(f pm,::: §COD F\): r/ y. -=- 1- )
5

f/2 14epstein/Math166/2011c_166... · 2011. 11. 16. · I I ~ [F8£. flJtJS /2XkfY\ "3 . aJrELu ('X/ li\t)v0-=(z.t)-3-t.-

Jan 21, 2021

Download

Documents

dariahiddleston
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: f/2 14epstein/Math166/2011c_166... · 2011. 11. 16. · I I ~ [F8£. flJtJS /2XkfY\ "3 . aJrELu ('X/ li\t)v0-=(z.t)-3-t.-<S) ll~) t . a . V1 . d. ~ anL-J . 112 ® (p..") 5::. 0

EXAM ~ lElA)

h0WCE (D fert = 000 ~( o~(o X 1+12) = ~~~ I iiZq b8 -~~2- +3

F pC 1+ r-c)-(Qoo( 1- IO~Lyenf2-) $ ~~920

~ N -6)1 9 g~ fY(Jf)M S

b) DO 6l =- $~200 ) ~~O -~~ ~~200 lJYl VY~

c) 4000 ~L J ~ -= ~O ) 20 to ~ )f2 6daM~ ~) 0JAteuro L - 20 =- 3~5 ) n~ - =3Cfco J I ~L1) -= 14 I b

e) N= ~~-1)- 5ltg prrrr LEF- Pm - 00 I~ V- R)=- 0 ~ ~ 341L 152shyJV- ~ (WM+-~ouowe) P)Y~d-

reg N ~5)( d- )mT-= ()OQ rr-- $ aL lt6 )330 1lt1 -g 1 - (p fv~ 0 pJ -==- ~ PI 2shy

reg N-c q mio fXJ~COo ~--~S fV~ 0 ~ $q~~l2D~d- p~ - ~ J = I

reg N-=- x~ tYT3coo I == l1 R)~ ~ -)l cp) J1 ~ 1 09 ~ $L235 VVI ~ -90=0 ~)lt2 L ~ ~ It4-h I(f

pm sectCOD F) ~-~r y -=shy 1shy

)

E-tf-(l(o )L-J =~ (o~tS~D ~~

f--ff (~ B ) 3 (os) Z 10 3

G) N 9 tmr- 0 r -= 5 I i-fo qOJtJ

I - ~ ~ - - ~~~d~ P~ 1(XX)O I - SWI+ h hll ~ = -- 5 1 3100

reg ~O (000 ~ r ~ ~ $4l-hooo d~OX~~

~ (I~nu J~O)OOO -~lOOO -==-~1~l 000

O~ N-40)(I~l=Ltili ftYlj-= ~ -7 lO~ 4~ 1-= CoI~ fU ~ 0 (OOS3)x48Q - lp OOD N-=(llc 000 PY=-12 3oCopo(o 4VVYl (k7~

~ 1(0 lOOD 0 ~31~ -= ~tI~4 M vn~ 1005t13 - q~~ ~ $$L1~ 1-0 ~l ClTI lovv

C) ~ = Ly8Q - J0 XJ~= 3~ 0 Pmr ~fftU~v~ pmT-=- l00 gt Jf ~ I -=-- ~ t~ 0J-~ (Jj-~ ~~~ ~QLl~h(9vJt r(middot~

) ~L)~ 3~1Q~ ( ()A() 13) Slo~ 14~)EQ ~ ~~OO(O - ltJaP5 13~ $51 stoLt- g

d) f- 3(00 ~Prnr$IO~3~ ) InT PA-ID =- $2J~) )~oL10

e) N-=-~ttO ~Prnr=$IqJ51) lIJIPAID==$133~1tp~O ~Co

~ N~ 5 X310S PmT-o I Lf fU - ~ ~--T 38Lt I tt~ pV-= 150 rllt ~ 3lS

jC4 ~ ~ fbi- relvllllV4 bull fu 1tWAV~ PlaquoVP J ~0 evyvfMAJ WY 0vv C1rp n~ 11u ~ ou WI) 9L u ffiiJ ~ ~1 10 -0 fJa~ ~oooX 03)1 (gtI~O

r -= 20 Pn1r 2000 ) if 31 5) ~ Lt- Y- ~ fV ~ --- shy

Xcoco ~~ 1shy

I I ~ [F8pound flJtJS

2XkfY 3 aJrELu

(Xlit)v0-=(zt)-3-t-ltS) ll~) t a V1 d ~ anL-J 112shy

reg (p) 5 0 ) t 0 So (-rgt ) 0 ) I)) VJ eo-~Gt (g) G o)t ~ o) 3(J-l ) o)-=- (-L))O)) l-- e fYfd (c) S-=-) t=-o $0(-1)-+)) JO)=- (-l)-) )0) rJo(Drred (D) s= ) t ~ So - 4 ) - ) ) ) VJ c

reg C~M g carts qtxO~t-~1o00~ t )1 JOO 2 =toltOCO ~ ~~ I)+- Vans 3Xi- ~~ i- 7 -= 413 ~- ~ ~vans i

( -y Z 7

r~ tAl J1 J C2l rre~ Go -3 ol X-3t 0 3 ~ 1 4~J [GO) ~ 0J ~-T2i - b

(rx-1I7t)~ 3t)b-(t) t) t ~ 1fef mltA11 ttu1S

t 0 =- o (c J 0) ~~ 0 etirrs) (ova Yl5 ayJ 0 tYl- Vtt n ~ t = ~ (3) t1) ) 13 3 (Arts -4 Var)gt WYd yY)-Vttrw t--~ - ( (p ) ~)~) 16v 0 (tIrrs) d OtY)S ()H() ~ rY- ~ns b 3 ~ (~ ) 0 ) 3) ~ 1 0 3gt 1II

rfi) U ~ -t-~ 0 2 3 7Ylinlla f)5 ) St co r6 )J( ( -7t VtLn5

reg ~ - ~ ta4thl S 0 ~l ~ X + I 5M I 5 J-h lIM-h ~ ~ ~ QXj~lI) ampt- SW3 e - ~A~ I (8~~)

0~s i 211- ~ ~Me tb_ii-~~ 5l t

P GL 5

CD 1- (3 =[ j ~l l ~ -r s t Q ltSL

8 middot A ~ R[ 5 8] T loO 151 == 6~ - R r J N5

I

2- S L~~ 50J m L (AA)n ~)( 00 +c1145 = tzr1L ~

rr-5 r b-and s~kf ~rJ Mti nx0 ~ k1 ~ cd rood ~

P~~h5t1~ ~~~

~ Ar~ ( B) ) ~ Rmots rntr tt2 a1- eCtch sf-o ~x ~ D ~ X6 -7 - Xb - XU - X ( -tI)

(f) -~ -I (- 2~) (B-tr)-l X

reg [0- -~II 1- 4r b - Q 91 t-L ~b - fCA-4 ~tLbl r~ ~l c1 d-J LeoJ t 1 L~ -- 0 1 l2r-~c ol--oj t~ -3J

~~1-~ = ~ ~~~-~ ~+~b-L ~ b~j2

-~-t4c=-~ A C - ri=-3

(i) 91 ~ l X 3) ~ o(3x3)( 0 )1)1 PossSpound B R S 6 (S

GXF (r3)(3~) $( i( )I )

~~ 3)( F~ ~ ~( ) ~( )

reg 4) pf~ b) (ox ltJ ~) J)(E oG L ~ s~r

J) l7X 1) ( ) () 1 ~ e) (~~foj ~~l) ~ Co~l

Page 2: f/2 14epstein/Math166/2011c_166... · 2011. 11. 16. · I I ~ [F8£. flJtJS /2XkfY\ "3 . aJrELu ('X/ li\t)v0-=(z.t)-3-t.-<S) ll~) t . a . V1 . d. ~ anL-J . 112 ® (p..") 5::. 0

E-tf-(l(o )L-J =~ (o~tS~D ~~

f--ff (~ B ) 3 (os) Z 10 3

G) N 9 tmr- 0 r -= 5 I i-fo qOJtJ

I - ~ ~ - - ~~~d~ P~ 1(XX)O I - SWI+ h hll ~ = -- 5 1 3100

reg ~O (000 ~ r ~ ~ $4l-hooo d~OX~~

~ (I~nu J~O)OOO -~lOOO -==-~1~l 000

O~ N-40)(I~l=Ltili ftYlj-= ~ -7 lO~ 4~ 1-= CoI~ fU ~ 0 (OOS3)x48Q - lp OOD N-=(llc 000 PY=-12 3oCopo(o 4VVYl (k7~

~ 1(0 lOOD 0 ~31~ -= ~tI~4 M vn~ 1005t13 - q~~ ~ $$L1~ 1-0 ~l ClTI lovv

C) ~ = Ly8Q - J0 XJ~= 3~ 0 Pmr ~fftU~v~ pmT-=- l00 gt Jf ~ I -=-- ~ t~ 0J-~ (Jj-~ ~~~ ~QLl~h(9vJt r(middot~

) ~L)~ 3~1Q~ ( ()A() 13) Slo~ 14~)EQ ~ ~~OO(O - ltJaP5 13~ $51 stoLt- g

d) f- 3(00 ~Prnr$IO~3~ ) InT PA-ID =- $2J~) )~oL10

e) N-=-~ttO ~Prnr=$IqJ51) lIJIPAID==$133~1tp~O ~Co

~ N~ 5 X310S PmT-o I Lf fU - ~ ~--T 38Lt I tt~ pV-= 150 rllt ~ 3lS

jC4 ~ ~ fbi- relvllllV4 bull fu 1tWAV~ PlaquoVP J ~0 evyvfMAJ WY 0vv C1rp n~ 11u ~ ou WI) 9L u ffiiJ ~ ~1 10 -0 fJa~ ~oooX 03)1 (gtI~O

r -= 20 Pn1r 2000 ) if 31 5) ~ Lt- Y- ~ fV ~ --- shy

Xcoco ~~ 1shy

I I ~ [F8pound flJtJS

2XkfY 3 aJrELu

(Xlit)v0-=(zt)-3-t-ltS) ll~) t a V1 d ~ anL-J 112shy

reg (p) 5 0 ) t 0 So (-rgt ) 0 ) I)) VJ eo-~Gt (g) G o)t ~ o) 3(J-l ) o)-=- (-L))O)) l-- e fYfd (c) S-=-) t=-o $0(-1)-+)) JO)=- (-l)-) )0) rJo(Drred (D) s= ) t ~ So - 4 ) - ) ) ) VJ c

reg C~M g carts qtxO~t-~1o00~ t )1 JOO 2 =toltOCO ~ ~~ I)+- Vans 3Xi- ~~ i- 7 -= 413 ~- ~ ~vans i

( -y Z 7

r~ tAl J1 J C2l rre~ Go -3 ol X-3t 0 3 ~ 1 4~J [GO) ~ 0J ~-T2i - b

(rx-1I7t)~ 3t)b-(t) t) t ~ 1fef mltA11 ttu1S

t 0 =- o (c J 0) ~~ 0 etirrs) (ova Yl5 ayJ 0 tYl- Vtt n ~ t = ~ (3) t1) ) 13 3 (Arts -4 Var)gt WYd yY)-Vttrw t--~ - ( (p ) ~)~) 16v 0 (tIrrs) d OtY)S ()H() ~ rY- ~ns b 3 ~ (~ ) 0 ) 3) ~ 1 0 3gt 1II

rfi) U ~ -t-~ 0 2 3 7Ylinlla f)5 ) St co r6 )J( ( -7t VtLn5

reg ~ - ~ ta4thl S 0 ~l ~ X + I 5M I 5 J-h lIM-h ~ ~ ~ QXj~lI) ampt- SW3 e - ~A~ I (8~~)

0~s i 211- ~ ~Me tb_ii-~~ 5l t

P GL 5

CD 1- (3 =[ j ~l l ~ -r s t Q ltSL

8 middot A ~ R[ 5 8] T loO 151 == 6~ - R r J N5

I

2- S L~~ 50J m L (AA)n ~)( 00 +c1145 = tzr1L ~

rr-5 r b-and s~kf ~rJ Mti nx0 ~ k1 ~ cd rood ~

P~~h5t1~ ~~~

~ Ar~ ( B) ) ~ Rmots rntr tt2 a1- eCtch sf-o ~x ~ D ~ X6 -7 - Xb - XU - X ( -tI)

(f) -~ -I (- 2~) (B-tr)-l X

reg [0- -~II 1- 4r b - Q 91 t-L ~b - fCA-4 ~tLbl r~ ~l c1 d-J LeoJ t 1 L~ -- 0 1 l2r-~c ol--oj t~ -3J

~~1-~ = ~ ~~~-~ ~+~b-L ~ b~j2

-~-t4c=-~ A C - ri=-3

(i) 91 ~ l X 3) ~ o(3x3)( 0 )1)1 PossSpound B R S 6 (S

GXF (r3)(3~) $( i( )I )

~~ 3)( F~ ~ ~( ) ~( )

reg 4) pf~ b) (ox ltJ ~) J)(E oG L ~ s~r

J) l7X 1) ( ) () 1 ~ e) (~~foj ~~l) ~ Co~l

Page 3: f/2 14epstein/Math166/2011c_166... · 2011. 11. 16. · I I ~ [F8£. flJtJS /2XkfY\ "3 . aJrELu ('X/ li\t)v0-=(z.t)-3-t.-<S) ll~) t . a . V1 . d. ~ anL-J . 112 ® (p..") 5::. 0

I I ~ [F8pound flJtJS

2XkfY 3 aJrELu

(Xlit)v0-=(zt)-3-t-ltS) ll~) t a V1 d ~ anL-J 112shy

reg (p) 5 0 ) t 0 So (-rgt ) 0 ) I)) VJ eo-~Gt (g) G o)t ~ o) 3(J-l ) o)-=- (-L))O)) l-- e fYfd (c) S-=-) t=-o $0(-1)-+)) JO)=- (-l)-) )0) rJo(Drred (D) s= ) t ~ So - 4 ) - ) ) ) VJ c

reg C~M g carts qtxO~t-~1o00~ t )1 JOO 2 =toltOCO ~ ~~ I)+- Vans 3Xi- ~~ i- 7 -= 413 ~- ~ ~vans i

( -y Z 7

r~ tAl J1 J C2l rre~ Go -3 ol X-3t 0 3 ~ 1 4~J [GO) ~ 0J ~-T2i - b

(rx-1I7t)~ 3t)b-(t) t) t ~ 1fef mltA11 ttu1S

t 0 =- o (c J 0) ~~ 0 etirrs) (ova Yl5 ayJ 0 tYl- Vtt n ~ t = ~ (3) t1) ) 13 3 (Arts -4 Var)gt WYd yY)-Vttrw t--~ - ( (p ) ~)~) 16v 0 (tIrrs) d OtY)S ()H() ~ rY- ~ns b 3 ~ (~ ) 0 ) 3) ~ 1 0 3gt 1II

rfi) U ~ -t-~ 0 2 3 7Ylinlla f)5 ) St co r6 )J( ( -7t VtLn5

reg ~ - ~ ta4thl S 0 ~l ~ X + I 5M I 5 J-h lIM-h ~ ~ ~ QXj~lI) ampt- SW3 e - ~A~ I (8~~)

0~s i 211- ~ ~Me tb_ii-~~ 5l t

P GL 5

CD 1- (3 =[ j ~l l ~ -r s t Q ltSL

8 middot A ~ R[ 5 8] T loO 151 == 6~ - R r J N5

I

2- S L~~ 50J m L (AA)n ~)( 00 +c1145 = tzr1L ~

rr-5 r b-and s~kf ~rJ Mti nx0 ~ k1 ~ cd rood ~

P~~h5t1~ ~~~

~ Ar~ ( B) ) ~ Rmots rntr tt2 a1- eCtch sf-o ~x ~ D ~ X6 -7 - Xb - XU - X ( -tI)

(f) -~ -I (- 2~) (B-tr)-l X

reg [0- -~II 1- 4r b - Q 91 t-L ~b - fCA-4 ~tLbl r~ ~l c1 d-J LeoJ t 1 L~ -- 0 1 l2r-~c ol--oj t~ -3J

~~1-~ = ~ ~~~-~ ~+~b-L ~ b~j2

-~-t4c=-~ A C - ri=-3

(i) 91 ~ l X 3) ~ o(3x3)( 0 )1)1 PossSpound B R S 6 (S

GXF (r3)(3~) $( i( )I )

~~ 3)( F~ ~ ~( ) ~( )

reg 4) pf~ b) (ox ltJ ~) J)(E oG L ~ s~r

J) l7X 1) ( ) () 1 ~ e) (~~foj ~~l) ~ Co~l

Page 4: f/2 14epstein/Math166/2011c_166... · 2011. 11. 16. · I I ~ [F8£. flJtJS /2XkfY\ "3 . aJrELu ('X/ li\t)v0-=(z.t)-3-t.-<S) ll~) t . a . V1 . d. ~ anL-J . 112 ® (p..") 5::. 0

P GL 5

CD 1- (3 =[ j ~l l ~ -r s t Q ltSL

8 middot A ~ R[ 5 8] T loO 151 == 6~ - R r J N5

I

2- S L~~ 50J m L (AA)n ~)( 00 +c1145 = tzr1L ~

rr-5 r b-and s~kf ~rJ Mti nx0 ~ k1 ~ cd rood ~

P~~h5t1~ ~~~

~ Ar~ ( B) ) ~ Rmots rntr tt2 a1- eCtch sf-o ~x ~ D ~ X6 -7 - Xb - XU - X ( -tI)

(f) -~ -I (- 2~) (B-tr)-l X

reg [0- -~II 1- 4r b - Q 91 t-L ~b - fCA-4 ~tLbl r~ ~l c1 d-J LeoJ t 1 L~ -- 0 1 l2r-~c ol--oj t~ -3J

~~1-~ = ~ ~~~-~ ~+~b-L ~ b~j2

-~-t4c=-~ A C - ri=-3

(i) 91 ~ l X 3) ~ o(3x3)( 0 )1)1 PossSpound B R S 6 (S

GXF (r3)(3~) $( i( )I )

~~ 3)( F~ ~ ~( ) ~( )

reg 4) pf~ b) (ox ltJ ~) J)(E oG L ~ s~r

J) l7X 1) ( ) () 1 ~ e) (~~foj ~~l) ~ Co~l