infi2HW04

# infi2HW04 - 4 A4 'qn milibxz oeilb - 104281 11 - 2 itpi`...

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4 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 2007 xanvcl 11 :dybd jix`z A 4 lcebn xiip lr yibdl yi .qxewd ly mi`zd cg`l ec`n` oiipaa qt` dnewa dybdd :zxekfz sca jxev oi` .oeilib xtqne ,f"z ,zeny xexiaa oiivl `p .wcedn yibdl `p .mixqlw e` zeiwy `ll .xry 1 libxz aexiwd zgqep zeliril dlabn `vnp df libxza . [0 , 1] rhwa ziliaxbhpi` divwpet f ( x ) idz a onqp aexiwd zgqep ly d`ibyd z` . R 1 0 f ( x ) dx lxbhpi`d z` jixrdl zpn lr 1 n n k =1 f ( k n ) . 1 n n k =1 f ( k n ) - R 1 0 f ( x ) dx :i"r dpezp `ide E ( n ) . n → ∞ xy`k 1 n n k =1 f ( k n ) R 1 0 f ( x ) dx ik egiked .` reaw miiwy egiked . r 6 = 0 - e f ( x ) = rx + s ,xnelk ,dreaw `l zix`pil divwpet f ( x ) idz .a . | E ( n ) | ≥ C n y jk C . | E ( n ) | ≥ C n y jk C reaw miiwy egiked . f ( x ) = x 2 gipp .b .aexiwd zgqep i"r mincew mitirqn f ( x ) xear R 1 0 f ( x ) dx z` aygl mipiipern ep`y gipp .c jixv n lecb dnk ( | E ( n ) | < 10 - d y xnelk) dcewpd ixg` zextq d ly weic lawl zpn lr ?zegtl zeidl 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 Winter '08 term at Technion.

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infi2HW04 - 4 A4 'qn milibxz oeilb - 104281 11 - 2 itpi`...

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