07WbSol - 30 . 5 . 2008 'a cren ,g"qyz sxeg ,2 itpi`a...

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Unformatted text preview: 30 . 5 . 2008 'a cren ,g"qyz sxeg ,2 itpi`a dpigad oexzt ipinipa a`ei :dxend myd aezkle cala legk e` xegy hra ynzydl `p .xfr xneg meya ynzydl oi` .zery yely dpigad jyn .mkicrv z` ahid ehxte ewnp .cenr lk y`xa ...100 "wx" `ed ilniqknd oeivd j` ,103 `ed llekd cewipd .sirq lka riten cewipd !dglvda . 1 dl`y .qpkzn ∑ a n xehdy jk zcxei zipehepen ziaeig dxcq { a n } idz (10%) ( i ) . lim n →∞ na n = 0 ik egiked lxbhpi`dy jk [0 , ∞ ) lr zcxei zipehepen ziaeig divwpet f idz (5%) ( ii ) . lim x →∞ xf ( x ) = 0 ik egiked .qpkzn R ∞ f ( x ) dx llkend llkend lxbhpi`dy jk (0 , 1] lr zcxei zipehepen ziaeig divwpet f idz (5%) ( iii ) . lim x → + xf ( x ) = 0 ik egiked .qpkzn R 1 f ( x ) dx okle , n 2 a n ≤ ∑ n j = [ n 2 ] a j ik zpzep zeipehepend ( i ) .daeyz ≤ na n ≤ 2 n X j = [ n 2 ] a j ≤ 2 ∞ X j = [ n 2 ] a j → .qpkzn xeh ly apfk okle , R x x/ 2 f ( t ) dt ≥ x 2 f ( x ) ik lawp zeipehependn ( ii ) xf ( x ) ≤ 2 Z x x/ 2 f ( t ) dt ≤ 2 Z ∞ x/ 2 f ( t ) dt → .qpkzn lxbhpi`d ik....
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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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07WbSol - 30 . 5 . 2008 'a cren ,g"qyz sxeg ,2 itpi`a...

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