infi2HW2 - 2 A4 'qn milibxz oeilb - 104281 - 2 itpi`...

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Unformatted text preview: 2 A4 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 27.12.2006 :dybd jix`z lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz z`e cinlzd my z` xexiaa oiivl `p .micigia dybdd .wcedn yibdl `p .mixqlw e` zeiwy `ll .xry sca jxev oi` .f"z xtqn : 1 libxz .mi`ad milxbhpi`d ly zeqpkzd ewcia 1 ex -1 dx .1 x 0 1 dx .2 0 1-cos x 1 dx .3 0 1-x4 arctan x dx .4 x 1 dx .5 1 1+[x]2 x6 dx .6 1 ex 2 e-x dx .7 - : 2 libxz . - e mixhnxtd t"r miqpkzn milxbhpi`d izn e`vn dx 2 - (cos x) .1 2 log(1+x2 ) .2 x 0 dx dx .3 1 x (log x) : 3 libxz oke In = n 1 f (x)dx :onqp .xcazn 1 f (x)dx ik oezp .[1, ) lr zcxei zipehepen .zqpkzn un = Sn - In :egiked f (x) 0 n .Sn = k=1 f (k) - log n .1 .qpkzn 1 1 + 2 + 1 + + 3 1 n ik e`xd .2 : 4 libxz lxbhpi`d ik e`xd .f (x) = x 0 sgn(sin t)dt :onqp .sgn(0) =0 - e x=0 lkl sgn(x) = .qpkzn x idz |x| f (x) dx x 0 1 : 5 libxz .qpkzn 0 sin(x2 )dx : ik egiked 6 libxz :mixehd mekq z` eayg n=1 1 log(1 + n ) .1 1 n=1 9n2 +3n-2 .2 : 7 libxz .mixehd ly zeqpkzd ewca 1 n=3 n log n(log log n)2 .1 2462n n=1 135(2n+1) .2 1 n=2 (log n)n .3 1 1 n=1 n1+ n .4 1 sin( n ) .5 n=1 n - n n=1 e n=1 log n .6 .7 .8 n( n - 1), > 1 n=1 (1 - cos( )) n : 8 libxz :egiked .Sn = n k=1 an :onqp .iaeig xeh an .1 .2 .qpkzn ( an (Sn )2 an 1+an an (Sn )2 qpkzn xcazn an an : an :fnx) .qpkzn Sn Sn-1 9 libxz mirvennd oeieeiy i`a eynzyd :fnx) .qpkzn an 3/4 xehd ik e`xd .qpkzn iaeig xeh n an idi .(qpkzn xeh i"r meqg xehdy ze`xdl zpn lr uxeey-iyew oeieeiy i` e` 2 : 10 libxz :egiked .f (0) > 0 oke f (0) = 0 :miiwzn .qt`a dxifbe [-1, 1] lr zxcben n=1 n=1 1 f(n) f (x) .1 .2 .xcazn .qpkzn 1 f ( n2 ) 3 ...
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This note was uploaded on 06/27/2008 for the course MATH Infi 2 taught by Professor Benyamini during the Winter '08 term at Technion.

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infi2HW2 - 2 A4 'qn milibxz oeilb - 104281 - 2 itpi`...

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