infi2HW3 - 3 'qn milibxz oeilb - 104281- 2 itpi` .(ef dryl...

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Unformatted text preview: 3 'qn milibxz oeilb - 104281- 2 itpi` .(ef dryl jenq sq`p libxzd !xg`l `l `p) mixdva 12 : 00 dry cr -- 17 / 1 / 2007 :dybd jix`z A 4 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 : 1 libxz ik e`xd . f ( x )- l [ a,b ) rhwa zizcewp zeqpkzne ( a,b )- a y"na zeqpkzn ,zetivx f n ( x ) .1 . [ a,b )- a dtivx f ( x ) . f n ( x ) = n q sin( e- 1 x 2 ) dxcqd xear (0 , ∞ ) rhwa y"nae zizcewp zeqpkzd ewca .2 : 2 libxz . f ( x )- l y"na zeqpkzn g n ( x ) ik e`xd . g n ( x ) = n R x + 1 n x f ( t ) dt xicbp . R- a y"na dtivx f ( x ) ( f ( x ) = n R x + 1 n x f ( x ) dt :fnx) : 3 libxz :onqp . 0 = f (0) = lim x →∞ f ( x ) zniiwne dreaw dpi` , [0 , ∞ ) lr dtivx f ( x ) g n ( x ) = f x n ,h n ( x ) = f ( nx ) .y"na `l j` qt`d zivwpetl zet`ey h n ( x )-e g n ( x ) ik e`xd .1 .y"na qt`d zivwpetl zt`ey g n ( x ) · h n ( x ) ik e`xd .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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infi2HW3 - 3 'qn milibxz oeilb - 104281- 2 itpi` .(ef dryl...

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