infi2HW5 - 5 A4'qn milibxz oeilb 104281 2 itpi`:dybd...

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Unformatted text preview: 5 A4 'qn milibxz oeilb - 104281 5/6/2006 - 2 itpi` :dybd jix`z .(ef dryl jenq sq`p libxzd !xg`l `l `p) mixdva 12 : 00 dry cr -- lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz z` xexiaa oiivl `p .micigia dybdd .(!zekiq wcdna) wcedn yibdl `p .mixqlw e` zeiwy `ll .xry sca jxev oi` .f"z xtqn z`e cinlzd my : :qt`l qpkzn , 1 libxz log(2) enekqy , (-1)n+1 n=1 n ,uipaiil xeh ly `ad xeciqdy e`xd 1- 1 1 1 1 1 1 1 1 1 1 - - - + - - - - + + 2 4 6 8 3 10 12 14 16 5 Sn = n k=1 z` aygl witqn dnl exiaqd .xeciqd xg`l xehd ly iwlgd mekqd :ik e`xde ak S5n idi :dkxcd ly leabd 2n S5n = k=1 (-1)k+1 1 + k 2 n k=1 1 1 1 - log(n) - + log(4n) + [log(n) - log(4n)] k k 2 k=1 4n : . 2 libxz .1 (0, 1] . lr zexcbend fn (x) = x n x log n 1 n2 x xear y"na zeqpkzd ewca [1, ) rhwa n=1 log 1 + xear y"na zeqpkzd ewca .2 xehd xear y"na zeqpkzd ewcae zeqpkzd megz e`vn .3 . x2 n-1 n=1 (-1) (1+x2 )n : . 3 libxz f (x) - l y"na zeqpkzn gn (x) ik e`xd . gn (x) = n 1 x+ n x f (t)dt xicbp . R - a y"na dtivx f (x) : :onqp . 4 libxz 0 = f (0) = limx f (x) gn (x) = f zniiwne dreaw dpi` , [0, ) lr dtivx f (x) x , hn (x) = f (nx) n .y"na `l j` qt`d zivwpetl zet`ey hn (x) -e gn (x) ik e`xd .1 .y"na qt`d zivwpetl zt`ey gn (x) hn (x) ik e`xd .2 1 : :xicbp . 5 libxz .y"na zqpkzn x=0 gn (x) lkl dxcqd ik e`xd . |f (x)| < |x| [-1, 1] gn+1 (x) = f (gn (x)) zniiwne lr zxcben - e f (x) g0 (x) = f (x) : 6 libxz .1 f (x) ik e`xd . f (x) - l [a, b) rhwa zizcewp zeqpkzne (a, b) - a y"na zeqpkzn fn (x) . [a, b) - a dtivx . fn (x) = n2 x2 1+n2 x2 dxcqd xear (0, 1) rhwa y"na zeqpkzd ewca .2 : zlawznd divwpetd df megza ik e`xd 7 libxz xear 1 n=1 nx ly zeqpkzdd megz z` e`vn x 0 .dtivx 2 ...
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infi2HW5 - 5 A4'qn milibxz oeilb 104281 2 itpi`:dybd...

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