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Sp94FinalSol - SP 94 EGN 3421 F INAL Name)0 ANY 4...

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Unformatted text preview: SP 94 EGN 3421] F INAL Name _ [)0 ANY 4 PRUBLEMS [Check the hex next In the problem if you want it graded} Shaw All Wnrk! Use Only Metheds Distussed In Class! [II PrelJlem 1 {25 ptsl all Estimate .i sin [1): fl :1] Using Tra peseidal lntegratien with H] equally spaced intervals. B} Using Simpsnns lfl Rule with l'l]I equalljr spaced intervals. Fill in the fellewiug table to help with the calculations. Reund all calculatiens and calculater display numbers in 4 places after the decimal. i X; ‘1 II} [Ltlflflfl I}.l]fl'|}fl l 2 3 4 5 fi 7 8 9' 1H Ans. l [Trapezeidall = , [[Silnpsen’s] = D Prehlem 2 {25 pts} The folluwing integral is to he appruximated using Trapezoidal Integratiun. 41‘. 1= I[’i(x—2J‘+2x3]dx u 12 Let II1 represent the approximation to I when the interval {11,4} is subdivided into [1 equal sub-intervals. How Imam}r sub-intervals must there be so that the error |I-I,|isatmustm4. I 3 Ans. n= [3 Problem 3 {25 111:5} A quadratic Spline is to be fit thru the following points: {0,1}. {1,2}, {3,3}, {4,2}. The spline is given by h1x+c1 [153:5]. flx} = a2x1+b2x+e2 15x53 n3x3+h3x+e3 35x54 A system of 8 equations in the E unknowns b1,C1,fl;,h1,C},flJ-,h3,fl3 has been generated, Le. A; =_h_. The vectors 2; and 11 are given below. Find the coefficient matrix A. II:|' IE Ezbl 2 2 3 h; 3 1 2 I} I} El Problem 4 [25 pts) An unknown function generated the following data points: {on}, {1,1.6437L {35114451} A} Find the Newton Divided Difference interpolating polynomial fgtx}. B} An additional data point (2,5.4366] is arailahle. Estimate the error in 132.5}. C] The data points were generated from the function [{x} = item. Find the true error in f3[2.5]. AflS- A] refit} = B} Estimate of error in M25} = n C} True error in EELS} = El Problem 5 {25 pts} Solve the following system of equations by using a sequence of Elementary row operation on the augmented matrix until it has been reduced to its Echelnn form. w + x + 3 - z = 1 2w - x + 3:; «- 2.2 = -2 W + 3" - z = fl 2): + y l Ans.w= , x , 3F= , z= _ , __%; k.R9....fi.€h‘i*:_fa-_kChain"! [a +‘4n9'15-Lcr1fi._-_.-4e_193 ’rw‘rq +_§..,.__ __.__ firfli‘SHN fir”.- (i‘ 1*r 5., *9: n3 1447.. - ZK‘Rtfim finial} ___ “___- _ .. . . ..______E11..E?_'hm.a-*\°.fl .3?” Q.5xfi%_--TtfiI’.-_xr¥‘%__ _____ w. ELLflE '.-_ "'_“'_ __"_s“ 1.3.1.339. _:§u_.1__.1‘.'\ . 11. 71? _._\__L_—L._:g._:~__..~_. faxiks ‘1._\7‘L~.1_ __ . _. _ __*__, rt. _ _ : fl_9~$_5.mm_3_9}§fis?l§vu __‘3 1‘ _ _ _ _ _ _ _ h L n m _ m _ _ M. _ h g _ _ m . j . _ _ _ E H n _ _ . _+ 11.. u _ H1. _ _ _ _ .J _ _ _ ~ ST: _w n _ 1. q _ i _ i _ _H .1 _ .. _ .m 30—1. $1“ m_ _ u _ u. no u o- %.—- mgr-13*ch finiaxjufit firm :6“! "I ____(...‘=’...}_3.'}._]__L $11.13;)” ‘5. (1,1,) _ __ BL?E_ _\_d_ flu. arng _ __ ant} Srhfitfi _ __ - _ ___ ___ _ _ _ ___- _.. . ___ _ _ _ ___ _____ __ . J ).....pM5. . LEE- .métr an-‘tsnamm. wax. wk. }.Q.F_E_~..___ _ 1___m.a_ _g aw ml. zrs-stcfl ma “mate . __. _ _..“ii‘r_9_.f__...h.m amt. Lfi__._ur$fl qaxanwunfi mi‘__1~_?.;f. ._._ _ $9.9"?flri “5:393. 12-39.. mafia .~=~.‘3-‘ WE- 1: M» t.“ 1-:- 3%. fix: -11-}.1... _E-xmd ,WK. inn-We, uqu. _ ___ __j _ _.g._ _ __ mm __ __ _ 3L: 5 _ ___ *__- - ___. 9H 1:9 - _, "‘er 5&3)?! _..Frabtj: ~ 13.‘4~‘15L.1I__ 1, . _ _ _ ___..._- 5: WEN?“ 1-K . = t. W- ve- : _\ 3=_§J__ ___? ___ _ _m___.__ _‘l‘+:}# d. __1_* o ___- _ _ _ ___W#__* %_[.hh.fi,l--77.._.1.}'..g"’!~“~5Lihbflfifl. ~. .5-.a‘=rre-L _ m______.__r_.__ __1 "3 _._ ._ _ ._ ..____ __ 3L$.1.,f~..._j_fi.1_? ELM..,1_,_1.~.¥Y_1R..,%;3 =_ mild-LL ______ $1.7} __._ _ 5: a ._,.______‘_ 'fi' _._;SILigffi¢3$73:___.13;_E!R%§Z 5.2)? 31.. __=_ _2_-._1.1_q.3_._____ _ _______ __ _ 1 "' " _ .m _ 5:1 1-. 3.,1s_,_,_x+,_x,l _‘E_ ablagmm 1 .~ 9r 11:513., Ll ____*____ _ _. fi____Q__1;1._-_i-;‘* m fl.._1-_L.**flb,$__}fl_;1). __ _._.._________. ,__._ _fifl__:d 53.135739\_§1:LJ_LF_EF)__:____. _ h. _= 9.33% m1;n.;1n_j3_,.._ ._ ___.___. _ ___ _._M_H ____ _ ._ ____ __ . ___- _. (Efihnc-S'sjkfimx; "F 2.51:. fig) _EzLilizéfiméjfijzjj ,_ _.w mw. __ __ __ Leia-1:153 at_x._,H1b:L1+f)tI.-S.\ "- flank»- , . Irma. emf is Gus.) 4.1.115] = 8.115‘1~‘1-‘153<=» = “Ga—‘1‘??? D._J_. CI £3 _ . _ w = _ _ + u i _ K). .. n _ _ I. B ,0— b. _ _ _ _ _ _ _ _ uL. _ _ _ o_ i Q ...
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