Sect10.4 - [OJ-(p.11 H @ 3(1) = § ['1 octet ° ‘éxéz...

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Unformatted text preview: [OJ-(p.11 H @ 3(1) = § ['1 octet ° ‘éxéz Goscrx‘e Serces: z a ’ 2 z ’ - g - - 0° ; T Sh“ d1 1 E £00 dx — (f '10 d7. — _ o o O 9 I 2 7L . mm r = Iggmmn—Tfax = gll'x)Co$"idx O 0 ‘ x - M11 nTT - Z nrri - s. w - J _ _, ’ $3622 Z d1 g1. cos 3 d7. .. MT '3 Z ' o I , ¢ .é— fl. 3: (ml 4- J75 r1117 M W" “T2: " “MW-2 HT 5‘“ '2‘“ 0 o - 1 .' J, x a .- Zr C t “ "$1005ng 0 6 \ . 135 Paer £3 4E! 1W 3;, Edu:-d~l Ch]: 603 Lax -.__ M Z I szs a’/>+ flaw"?! —$§wgrt_17 D HTT z, 0 43/! E5)+ ice “Tr 27' “W MT -605 3 MT 37/ - ['77 SW7 ‘2“{3'Zgnw 2; MT MT “’7: : ‘2 F.) [fir 3m 1 [(an)‘3u/b(ym72) 7T2 VIZ :0 £50" Z bnsmg’gl I 04744] 436:): game Seats PercoaM 0 I L252; 2'2 2 ‘ i 00‘ Iggmm = 2811mm; :Sdt= it =l 0 o o 12 t ' 2 an _ as 2.1 .. 3. su; my a“: £00 €03 7 dx “9 2 dx "If 2 O o b O n even. - £- SW fl _ — n" 2’ — Z R$W3 11 odd HIT WI —- - 3 z ’ H , n= I) 5', 9 (703mb Saree; Pardod l/fl’ {/0er 4’ Section 10.4 Problem 23 part c > a:=n->2/n*sin(n*Pi/2)+4/(n*2*Pi)*(cos(n*Pi/2)—1); sin -1 1t 1 1 n - - 2 4 cos 2m: a:=.n—->2—-—+ 2 n n 1: > s :=m->Pi/4+sum(a (n) *cos (n*x/2) ,n=1 . .m) ; m 1 2 : 1 s:=m—->Z1t+ a(n)cos(§nx) 11:1 > plot (5 (10) ,x=-6*Pi. . 6*Pi); QCQ=3~>< O‘VLB even exfinwdn octoi ex‘tensrdr) A 6% Section 10.4 Problem 27 parts c and d > a:=n->6/(n*Pi)“2*(1-(—1)“n):b:=n->6/(n*Pi): > g:=m—>3/2+sum(a(n)*cos(n*Pi*x/3),n=1..m):h:=m->sum(b(n)*sin(n *Pi*x/3),n=1..m): > plot(g(10),x=-9..9); -8-8-4-202468 x Plots of other partial sums look basically the same. The sums with more terms have sharper corners and come closer to touching the x axis at x=—9,-3,3,9. > plot(h(10),x=-9..9); > plot(h(40),x=-9..9); l/OJH. I0 > ge:=m—>abs(g(m)—(3-x)):he:=m->abs(h(m)—(3-x)): > P1°t({ge(5),ge(10),ge(20)},x=0. .3); > evalf(subs(x=3,ge(5)));evalf(subs(x=3,ge(10)));eva1f(subs(x=3 Ige(20))); .1004167175 .06059282070 .03037111368 > plot({he(10),he(20),he(40)},x=0..3); > evalf(subs(x=0,he(10)));eva1f(subs(x=0,he(20)));eva1f(subs(x= 0,h6(40))); 3. 3. 3. For the even extension the maximum error seems to be always at x=3 and is decreasing as n increases. For the odd extension the maximum error appears to always be at x=0 and is always 3 (i.e. is. not decreasing as n increases). 'IO.‘-{f.392 (39) 2 vs W as an odd {anchovy Lax/UN pen‘od L41. 2! rm“! 8 ’ __—— x c £01) Cos 13 add i? an =th g 9‘00 60% gait: O ~2£ 2Q and ' ,- “.03 _ _\_ 42(1) 3% 21 IS eMA r) LA: 22 g 12(1) 5;”erde :3) ’21: 5" Suk "I? 2.2 (3?) Malaria) 091.21 9 1‘3 WM as an odd imam/Wm perm! Ll]. As .02» Problem 38/ also 1n=0, 1,2, z! w w M m an 0 l 1' 24 : gr} .L - it? b" 1 53(10st 6! dz + fie/fl fist!» fl d1: 12 fl 0 121*) n flTr?’ d zflgmwfifi 4379‘?” "21 3 o . I) t ,- w. “W =- fiht) Sm ELI d1 £(3)[ SwaV'iTeoS 82 (’0an 3m, ay]dg c) , ...
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This homework help was uploaded on 04/09/2008 for the course MATH 2400 taught by Professor Yoon during the Spring '04 term at Rensselaer Polytechnic Institute.

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Sect10.4 - [OJ-(p.11 H @ 3(1) = § ['1 octet ° ‘éxéz...

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