7.6 - 50 SHEETS 224/12 100 SHEETS 200 SHEETS 22441 22444...

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Unformatted text preview: 50 SHEETS 224/12 100 SHEETS 200 SHEETS 22441 22444 @232}. W 17:6 HEM/W. ermva é Szrfipsm’s fladle, 6mm . : Exad Valaa -' App/lax. Wide, [E usually unKnou/Iv, so arm/6 lsflw.’ (wordy 0F wumemc‘a/ Myriam/1052mm ls really sway of err/Ms g i haw much lug/Ur is [mm/Med 7‘0 make; 729:6 arm” smawm. Q. X 19?“: m2 % 0.093/4’7/3’06 : I Table 7.1 Errorsfor the left and right rule approximation to ff l dx = 1n 2 % 06931471806 Left rule overestimate l “53:1: Right rule ‘ underestimate l l Error in Error in left rule Figure 7.13: Errors in left and right sums 2The values in Table 7.1 are rounded to -l- decimal places; those in Table 7.2 were computed using more decimal places and then rounded. o znéreasa 7b by a, Fae-bar 07“ 5 each {M7}; v d/scass 54927 of err/“we . .. x4015 )5 underesr/mfia 5v erme 70 9 art , a a /7%06(j/) ofl/posim Slgfis 3 errazs 05 LfiS/fl/fi aura a; 54/77:; magfl/mdc ° 7’0 Ccmre/ 0mm) 7792a dye/aw % #1’5 49M /5 a gaad [déa/ M2: is 77%” J / WM_.-_.H._;1¢LA¢#0X. grabs! & 22-141 50 SHEETS ?? ‘1 2 “"9 cHErTS 5,\\ J' \ _ \nrjrmnx/ - — 22—144 200 SHEETS .1 / . . 2 Table 7.2 Rana oft/1e errors as n Increases for f1 % d3: Ratio of errors Ratio of errors I in left rule in right rule 0 ram 019 grams Sham/5 7%47‘ arm/e, deal/£57525 by a fichzm flF 5“ as 77 //76/"€a5?& {y flora/65 79/ (HS/M5 VOW“ WNW decreases by a 7%07‘6/ log /\/ 43 you lncrmre by a fizfia/ (77a N, a This 15 T/eue, w gem/raj . .. 0 FM LEFT 0% RléHT rules, each exfm dzyh‘ ‘ 05 accurng er/res /0 77/7768 fix: work. «We, 10W a Esec. 50 Sec '/7, Sec. Calculafor to comm 5«/&7s:ec z? 1 yea/e. ‘1 1 ~ I e L I fl_t,,_v,__._s_744i4%o7g2m2amnm_&w5 & 5212343 I95 _ Table 7.3 The errors for the trapezoid Midpoint /-' and midpoint rules for f; i dx error gagfzoid 4 Errorin midpoint rule \ fix) : % Figure 7.14: Errors in the midpoint and a w trapezoid rules o T/Q/‘HD <6 mm 41% much befifl’ #2419 M5 Co M/s - mum is fie #6/ 7%4/7 7704/9 , _ I /6i”/"0/€ 01D M/D/ ’5 é- /eIe/eo£ 070 T/ZHP/ Table 7.4 Ratios of the errors as 11 increases for ff % dx Ratio of errors in Ratio of errors in trapezoid rule midpoint rule A 23.84 24.95 25.00 . ,45 n Increases. by a “fie—for 0F 5') 2 Hm erme decreases by abouf 790ml“ 012 5 . This “N” reZaT/onshi‘p can be Show/v +0 hold no general. a Less wank 13 involved To gain CUiOH’MV decimd’ PiaCCu ~~ (0 Times We WOVK git/as 30% 2. mom digits 0% accumch 13¢ oilalfsmc Jen/vie, +0 fl ace connpr ti [/2 sec. ('0 5 Sec. to €003ec.R’/|Omin SO SHEETS .1 224112 100 SHEETS 22-144 200 SHEETS 22-141 ,/ Aflb \ - ( m _ .. :Z.le-.&/apmxwi_££boli£§_ mfiogfirzmsané _ V I v Obserm 7304+ 77%;) efmr baa 0pp05/76 51:9}? & arbour Mice, #06, mayo/fade, 0P Midpamf errar. a 77225 Suggests a, rue/307%! average, 070 70% Two Rules —— we/jhing mid/001M dank/y» will have a smaller arm/z, 3 SIMP(n) 2 Table 7.5 The errorsfor Simpson ’5 rule and the ratios Off/16 errors 2 —0.0001067877 ' 10 40000001940 50 —0.0000000003 550.15 632.27 o awry/es am much SmaZ/E/fl a Nam 7‘1047‘ H’s Lmfizilé fl Campfire 7‘0 OHM” Nt/ZS d/rzcr/y sm‘m here we may cam/447% f g? each endpa/m‘ p/z/S @3 Wi/d/mmfi. . A} N lflCVédSéS by 61 7975/0” 07C 5; wry/25 decrease éy 4": 000 a; 56,1 . lo ‘flmes Hm eXWa work 96W“ 4031910? 010 accumcg, I gmksg , A Haw 7%.; frm/ Depends an #m Mfan . (When farm/13 key/ales /V 5274756074 76976, 5/22 075 7‘75a gin/“0E, M 640/”) 07a 0w mgffiadd’. J": -ETS nq F m, 22-142 mm SHEETS “A re. .-, / ¥// 22-144 206 SHEETS a Imag/hé we, /eave A/ 6/)(66/ 4Q Cans/dew whaf flaming 0P Hx) Impac+ #66 accuracy. STee/oness 010 ap/X) afifiecv‘s ermfl. /7C 75 / 5/774 // ) /€SS erma [7C f / 162mg) Mara é/mfl . (Error depends on S/ia 0‘9 70’ W curvav‘um 0F fix) 6179560743 arm/e. if 75” Smaa) small, arm/f ha f” Jame ) meg firm” a firm depends on ma 07C f" QWW . {SIMPSON ' 1+ can be shown In a OOUYSé/ 1h humewtial anatys‘ls Hwt eer dapends an 8126 OrF 3d”) ...
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This note was uploaded on 03/26/2012 for the course MAC 2233 taught by Professor Smith during the Fall '08 term at University of Florida.

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7.6 - 50 SHEETS 224/12 100 SHEETS 200 SHEETS 22441 22444...

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