Question

Find the approximations , and for , and . Then compute the corresponding errors , and . (Round your answers to six decimal places. You may wish to use the sum command on a computer algebra system.) What observations can you make? In particular, what happens to the errors when is doubled?

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Answer 1

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So, he idpo'int vele ts Woen by 0-2Co-1)C0-3)+{O5) +f(0+)+co) t 0 2(6.11o +0.404915 g+ 0.8243606 + 1:4096 268+2. 2136428 0.9926208 Ag= he htappoxim ion methad s ven by 0-1012)+ (0314 fco4)+ f65)e6)¢f@9)+{o8) OO11051F+6.24428 +0.40495 +0.59329e t0.S243606f 6932912+1 409626+ 19&04 3 2 + 2 21 36 428 +2.918281 1139610 13 the lest aproox Tsu) dion melhol 6-1040-1+o2)c03)(04)+5)+f&x6 )+{Co) 010+ O OR9+0. 24428 +0.404953 + o 594 298+0 8243606 1.0982912+ 1'409626 tI. 400 4329+2.213642 &985tt 98.9

Proen bey the tra pesoidal ele is fo2ko2o2)+2fc03)+2{C0-4) +2{ (o53+] fo6)+24 Co3)+2 fcos) +2{ c0 ) +f0 2 93459 + l-648 21 00.221034 048561+O 8099151 2.186 5425+2 819253)+8. 560 965 +4 429 2g5 + 2. 418281 1-003690 he mdpoint ae ten S bnteunls O 05, 0 15, o25, o35 ase O 45, 0 55 65, 0.5, O S5,0.15 So he md pont ele ues o Co05)+Co-15o 25) +f(o35)+{045) Co55Co5)+flot5) + Cos5)+fcon5) 6998152 3 q 0 n20 1-0 A 6 05 20 Ine Rightappoxtaation mehod is Con5H fco+fC5)+f (02) +- t(05) 0) CL888901 he lebt appsoxim dion 6.05 46+c0 05)+tCo1 melhod 05) .73.2969)

ule ues the Peiosaday 1ed 20 H)+2 005)+2 401)+ - 05)+fo 1 le 00024 Subintesiwals ye he mid point yzale 0 025, 0.635, o.125 0.193 (o 025 1 O.O g99528 the thoelve apporimdhons be be low tablo Summeiges To LA O 99262 1- 61499 0429431»26599 ID 6 693821.13161o 998 152 1063696 20 l338 90 1:000924 32969 a 19538 From undemeutal calcules CleldCo)

go calalale he COTT espondtng EL, ER, ETand Em eTors EL ET EM Ittbio O 009339 -0. 286599 0.259053 6 132218 0.139610 0 00 3696 O 001848 10 O O033 O000462 20 6. 000924 33890.0 From the caleulations, make he folloon severl obceurens ). In all fou melhads, h appooximiene get more accurte shen be valzee o n gn Creases )he esO in be leht en pon appoxition and aprxthatel halve eton h velo amd bave opposste doubles ) he Trapezofdal md olhe too approxim ettens rdpotnt Rrles acuale ha he ase moe 4)he eOrS he Tompegodel Sms md appeas to decrea b and Md pont Rulee have oppoi be actor about 4 ohen the Valzea doubles the eror he mfdpoint Qule about bal be eotos qn Ihe Tmpeod Rele