infi2HW8 - 8 A4 'qn milibxz oeilb - 104281 - 2 itpi` :dybd...

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Unformatted text preview: 8 A4 'qn milibxz oeilb - 104281 - 2 itpi` :dybd jix`z .(ef dryl jenq sq`p libxzd !xg`l `l `p) mixdva 12 : 00 dry cr -- 30/6/2006 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 : :zeivwpetd xear 1 libxz x=1 dcewpa zxfbpd z` eayg F (x) = F (x) = x2 0 x 0 arctan( xt2 )dt tan(t - x)dt : .1 .2 2 libxz ik oezp . F (n) (x) z` e`vn . F (x) = x 0 f (t)(x - t)n-1 dt :mixicbn .dtivx f (x) : 3 libxz 1 :lxbhpi`d z` eayg I= 0 log(1 + x) dx 1 + x2 . I() = log(1+x) dx 1+x2 0 z` mcew eayg :fnx : 4 libxz 1 0 oalna zeiwlgd zexfbpd :zedfd z` egiked (-1)m m! xp (log x)m dx = p 1, m N (p + 1)m+1 zgkeda wiicl `p . zetivx f (x, p) = xp :divwpeta eynzyd :fnx !mi`znd : 5 libxz 1 :lxbhpi`d z` eayg a = 0, :miiwzn ik al eniye I(a) = 0 1 dx 0 (x2 +a2 )2 - e dx 2 + a2 )3 (x F (a) = 1 dx 0 x2 +a2 . zeivwpetd z` exicbd :fnx G(a) = I(a) = -1 G 4a (a) = -1 -1 ( F 4a 2a (a)) 1 : 6 libxz 1 :lxbhpi`d z` eayg I= 0 dx 1 + ex F (a) = 1 dx 0 1+aex :fnx : . 7 libxz ik oezp f (x0 , y0 ) = x0 :miiwzny jk (x0 , y0 ) dcewp zniiwy e`xd . R2 - a dneqge dtivx f (x, y) 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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infi2HW8 - 8 A4 'qn milibxz oeilb - 104281 - 2 itpi` :dybd...

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