iii f'!j - university of warwick · t~/~ s"n'""'p& id~q j iy~r;...

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j)no(;s;,s III f'!J COnIQcIS. o otrJ~@ IYlCfIAs . wa ew ic«: QC U/~ B 2. 22. iec-Lre,; : mondo.::J /7-/f ~e /S"-/6 /115.02 ThC/ //-/2 2 q &clur es / Ij J-narl.ed =»: me...,-/; (/S- /0 ) y ca r; lie" eM r-r, (go %) ASIJnrY>r?~/s : C;vero 0«-1 o~ mond J J wee;s 2 L( 6 ? ) / ) s;«: -!on~ et re due .bQc I: D0 /r7Or.d~s / 3frn w~t" i5 '-0 6/ e;; 10

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Page 1: III f'!J - University of Warwick · T~/~ S"N'""'p& Id~Q j IY~r; r:s.1l., 0-10 ~uRor---rtr OXI 'rt'I.-c, ~ o r-, Sc,A-e-rTl~ ~(' SO~VIV ObE'S.: III fbr:}€..- . [~ 1,] Us~ Ih~ N )

j)no(;s;,s III

f'!J COnIQcIS.

ootrJ~@ IYlCfIAs . wa ew ic«: QC U/~

B 2. 22.

iec-Lre,; : mondo.::J /7-/f~e /S"-/6 /115.02ThC/ //-/2

2 q &clures/ Ij J-narl.ed =»: me...,-/;

(/S- /0 ) y car ; lie" eM r-r, (go %)ASIJnrY>r?~/s : C;vero 0«-1 o~ mondJ J

wee;s 2 L( 6 ?) / )s;«: -!on~ et re due .bQc I:D0 /r7Or.d~s / 3frn

w~t" i5 '-0 6/ e;; 10

Page 2: III f'!J - University of Warwick · T~/~ S"N'""'p& Id~Q j IY~r; r:s.1l., 0-10 ~uRor---rtr OXI 'rt'I.-c, ~ o r-, Sc,A-e-rTl~ ~(' SO~VIV ObE'S.: III fbr:}€..- . [~ 1,] Us~ Ih~ N )
Page 3: III f'!J - University of Warwick · T~/~ S"N'""'p& Id~Q j IY~r; r:s.1l., 0-10 ~uRor---rtr OXI 'rt'I.-c, ~ o r-, Sc,A-e-rTl~ ~(' SO~VIV ObE'S.: III fbr:}€..- . [~ 1,] Us~ Ih~ N )

J't ={ (~,t).xCO)=Xo

j () (Y)osl CQ,f-eS

Page 4: III f'!J - University of Warwick · T~/~ S"N'""'p& Id~Q j IY~r; r:s.1l., 0-10 ~uRor---rtr OXI 'rt'I.-c, ~ o r-, Sc,A-e-rTl~ ~(' SO~VIV ObE'S.: III fbr:}€..- . [~ 1,] Us~ Ih~ N )

T~/~ S"N'""'p& Id~Q j IY~r; r:s.1l. , 0-10 ~uRor-- -rt r OXI 'rt'I.- c, ~ o r-, S c,A-e-rTl~ ~('

SO~VIV ObE'S.:

III fb r:}€..- .[~ 1,]

N ) N I

Us~ Ih~ Q bov-e -kr rrvu eS.5~'-<- ~~r/ :: z x'" xCf) -Iru~ >of'-<-hor)

\ ~ X::- XN{f) - -rr=:- le/t I soe~~on. ,I ( co•..h'rju..o<--<-s pIece WIS(,I ..ft'n.f!~ r- / 1c{ "c A {7~)

-[ z: J j~~~ +:0-.1 1 tIf.! "N '31'/'"

XN (I) =

/Xu (I) -:x (1)/ < s 1/ lE [S /]ne&<" 'j"'-2.s/'orJs are !he. SufJ'ecl of

nu.me~,(.~~ Q n••.':;S'(S ;;}r oh E!s..J] "Cl bs' S '!1 w;1!R j (Ve .1°,-< IOD-&c; Cl n~we"2r 1/'",,..,,..,,

Page 5: III f'!J - University of Warwick · T~/~ S"N'""'p& Id~Q j IY~r; r:s.1l., 0-10 ~uRor---rtr OXI 'rt'I.-c, ~ o r-, Sc,A-e-rTl~ ~(' SO~VIV ObE'S.: III fbr:}€..- . [~ 1,] Us~ Ih~ N )

Jlnolher {'o£ w'j -k sofve ODE S(Pi~~j~ o.p!'Dxl'rnaho0 scherY>e):

::cdl) == Xo t (Losl q d fie sj~rYJ~

:x'z 0) '" .::r~+ /' 1'(.::rJu) T) J[o. . . t-

~~ (I) = ~o -i: Jr( ::XR-,(<.} z)J[ (x)o

Page 6: III f'!J - University of Warwick · T~/~ S"N'""'p& Id~Q j IY~r; r:s.1l., 0-10 ~uRor---rtr OXI 'rt'I.-c, ~ o r-, Sc,A-e-rTl~ ~(' SO~VIV ObE'S.: III fbr:}€..- . [~ 1,] Us~ Ih~ N )

oCk'rle, f. TA.., ,,,leJrqfl c. slef> l2~lJr>3mo A'v q Ion: reCCt.ee I he re fct JOA l:Icoee n

ar.eq u.nder jie CL(rve err.cI (0/e)('O,t's

( A . fie o-e Ps ) . Thereh-e I ,.; is r:e<lJ onc iee/0 de h~e- :

j

--+-----+r-r~-- ~ = ( Ix) - Co n ,-L I r£ A c., j 0 "

b x

(~~r9~

/llOf'e oc/e r: we

" e.: ..:.: S lep

/

Page 7: III f'!J - University of Warwick · T~/~ S"N'""'p& Id~Q j IY~r; r:s.1l., 0-10 ~uRor---rtr OXI 'rt'I.-c, ~ o r-, Sc,A-e-rTl~ ~(' SO~VIV ObE'S.: III fbr:}€..- . [~ 1,] Us~ Ih~ N )

..If ~Q or" IUJo r~jrfo,..s a~cI Pc cl)ose ~~ JAG IS 0 reh"nernpr>{ of p

TAe srn~5;/ COrnn'lon r~i~~",/ DI"' Lorr-l~o"s is denokd PUQ

(Jhql woufc,/ k q se> lSf 'f 00,<0£"

kx- 1: £ f(x) dx ? .(A. t: Cl'( r,--fi-t:) r0f/ -~