Assignment 3

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Straighterline *

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250

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Computer Science

Date

Nov 24, 2024

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6

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lName lianna Belasco Coume MAC oçessor Oo. 3T0 6361629 |Oate & 23 lola923 2312 Creoge Kapkouls Assiqnnnent 3Computahons oh Riemann Bums. Palblem 3.6 A-I ln i tene inpintely ' (Oensi ) 3up D() max lA -1 ing Dlx)=min(A-1 A+I Uoper Riemann |uto,)e Sum Porth'hon mar(A-i ,A) (2i-;)=max(a-l,A)(Xi,- 20 max(A-1 ,A+1)·(Kn -,) =max(a-1' A +)( -c) ||L(,e) = min(A-l ,At).(i -X )amin (A-l,A+) (Xi-i ) > min(A-l ,A +) (Xn - o) Emin(A-1, A+):(d -c) u (o,P) =mmax (A- A+) (d-) = min (A- ,A+) - (d -c) L (0,P) Created with Scanner Pro
Poble 3.1 [i,5.s) Li inç) Si() + S () + S3(13) +Ss(13) ult ie) =3o () L( e) (u) + e,l) 3 Se =5 =1 Si = S.5 3 u(e,e) = $(4) +s.s()+ (-6)) A (-1) 13) L(E e) = (4) + (-63))t (-7)) + (-20) (13) Rblem 3.8 i ę xE [o,s) 5 l) =)3x La-x2 -23 3,4 i Si 2sup (x) -11q ine S (1) + a (1) uf,e) s.(3) t+ S, () 4 L(6 1e)= lo (3) + , () uct,e) = q(3) + 12 () L(R P) = + 1S() o(3) + (-14)() =-8 24 Created with Scanner Pro
10- |Pobsem3.9 ie x e (1,12] |e o,1,4 10 ,, 2 Iovsta u(A P) = s,() +Si(3) + Sa(G) t S3(i) + S4() L(R ) Lo()+ti(3)+lo(4)+ 3 0)+ ui) S= 4 S =- 3) + 10(6) + (-)() t (-4) () |L( P)= o)t (3) (-s)(6),t(-q)0)+ (-lo)) uCt, e) = t() Created with Scanner Pro
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Prololm Bil 0 Afuthon f is bounded Ca,b] Ron al1 zeCa,b] bounded M,N M sfox) 4 N M Such +het The Drdinate se e a functonouer nteval On ( -(x) E(x)) (3) A pant'hon an inteyal [a,b parhhon AS Set Parton nteval of )A soesialporhihon f an intevelKaequalparts parts pa,] |%i= a+i n b-9 X; 4 b-- = a n b-a n Created with Scanner Pro
Ie)heSupes value a Runction louer Roterva an braic heignt oe Ahe Aouest ina eamemtalb00e or eo,yaal 1e arph sup Px) Superior value over albsolute [aP] hen has Value an max max f(x) o The ngerior Tne alaebrac nterval line seamentbelou or eaucl yalue a oRunthion ouer heiart he to Over qaph La,p] ine a) inleciOr Value Uer 9 (o) minimum v aluo [o, +nen en eoolute =min x) has ower ine Pex) he 3uperioRectanglae aRunchion heSuperion base Ca,b] and. top Side the \awest Aouchina wer an intenual anale o over [arb aetande itth \ine 32ament above abae tleegraph not aboue te qroaph the cectcnale Superor ordinte Created with Scanner Pro
The ngenioRectange The ingerioc cectannle base oelo or a Runchon Ca.b] ouer nterual cectanale [a .b] Ofher hiahest and 4he S2amelnt eoual to araph inferior rectane ower a, b] (9)The Upper Riemann Sums a Runchon a Pachithon. Over lhe cpDermeMEnn the sianed area a he Por hion serior reetange Sup f(x) (ao)The Loser Riemann 3ums Bactihon Aunch'on P. .... , L(4,e) = <sx (3i -;) Signedareaap tle th inlerior inp fx) recteinale )TheDensihyPhenomenon Reols enu realnumbe +hene Ore insinite ononal end inrahonds densely peporot ed eraph Created with Scanner Pro
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