Infi2_hw3 - 3 oeilib -2007 aia` - (104281) 2 itpi` 13 : 00...

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Unformatted text preview: 3 oeilib -2007 aia` - (104281) 2 itpi` 13 : 00 ,2.5.2007 ,iriax mei :dybd jix`z xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz xexiaa oiivl `p .micigia dybdd .wcedn yibdl `p .mixqlw e` zeiwy `ll A4 lcebn .xry sca jxev oi` .oeilbd xtqn z`e ,f"z xtqn z` ,cinlzd my z` :ze`ad zexcqd leab z` (onix inekq i"r) e`vn .1 3n an = k=n 1 k k (`) bn = b a 1 8n 4n (a) k=1 egiked . f (x)dx = 0 ik oezp . [a, b] rhwa zilily . i`e ziliaxbhpi` :y jk rhwa f (x0 ) = 0 f (x) x0 idz .2 miiwy :mi`ad zepeieeiyd i` z` egiked .3 1 0 a 0 xe-x dx 0.47 a > 0 (`) sin x 1 - cos a dx x a (a) :mi`ad zeleabd z` eayg .4 x0 lim x 0 sin t2 dt log(1 + t2 )dt x x+a -t2 e dt x x+b -t2 e dt x x2 (`) miiaeig a, b lkl x lim (a) ziy`x .ziliaxbhpi` `id xehpw zveaw ly zpiivnd divwpetdy gikep df libxza :ze`ad zeveawd z` onqp .xehpw zveaw z` xicbp .5 3k-1 -1 Mk = i=0 3i + 1 3i + 2 , 3k 3k , k1 1 ote`ae C0 = [0, 1] onqp zrk .(migezt mirhw ly cegi` `id efk dveaw lk) :lynl . Ck = Ck-1 \ Mk 2 1 , 9 3 onqp iaihwecpi` C1 = 0, 1 3 2 ,1 3 , 1 3k 1 C2 = 0, 9 2 7 , 3 9 8 ,1 9 :zeidl zxcben xehpw zveaw (. mkxe`y mixebq mirhw 2k ly cegi` `ed Ck lk) C= k=0 Ck A A :d`ad divwpetd `id dveaw ly zpiivn divwpet A (x) = 1 xA 0 xA / 1 0 B 1 0 A ik egiked ABR k ik gipp (`) :(dying k"dqa) mi`ad zepeieeiy/zepeieeiyd-i` z` egiked (a) (1) 1 0 (2) 1 0 (3) 1 0 0 C C Ck = (4) 0 1 Ck = (5) 2 3 1 0 .ekxr z` eayge miiw C :y egiked (b) zveaw ly zecewpa weica dtivx dpi` xehpw zveaw ly zpiiprn dpekz oldl C - e dipn za dpi` xehpw zveaw :dxrd .miiw 'b sirqa lxbhpi`d z`f lka ;xehpw itl gezitay mixtqnd weica md dveawd ixa` :(df libxzl ziyeniy dpi` xy`) .mizye qt` zextiqd wx oda zeriten (ozip xy`k iteqpi` aizkae) yely qiqa .(!yely qiqaa 1 4 z` meyxl eqp) xehpw zveawl jiiy 1 4 ,lynl 2 ...
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This note was uploaded on 06/27/2008 for the course MATH Infi 2 taught by Professor Benyamini during the Spring '08 term at Technion.

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Infi2_hw3 - 3 oeilib -2007 aia` - (104281) 2 itpi` 13 : 00...

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