infi2HW03 - 3 A4 'qn milibxz oeilb - 104281 28 - 2 itpi`...

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3 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 2007 xanaepl 28 :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 . f ( x ) 0 ik oke [ a,b ] - a ziliaxbhpi` f ( x ) ik oezp f ( x ) < ε y jk I = [ α,β ] [ a,b ] rhw zz miiw ε > 0 lkl if` R b a f ( x ) dx = 0 m` ik e`xd .1 . x I lkl mipeieeiyd i` lk) R b a f ( x ) dx > 0 if` f ( x ) > 0 y miiwzn x [ a,b ] lkl m` ik egiked .2 .(miwfg .xehpw ly dnlae mcew sirqa jk myl eynzyd ;dprhd ly dlilyd z` egiked :dkxcd : 2 libxz `ed qt` ik egiked . 0 < x 1 lkl f ( x ) 1 2 x zniiwnd [0 , 1] lr dtivx divwpet f ( x ) idz : [0 , 1] a d`ad d`eeynd ly cigid oexzitd x = Z x 2 0 f ( t ) dt : 3 libxz : a,b > 0 xear `ad leabd z` eayg lim x →∞ R x + a x e t 2 dt R x + b x e t 2 dt :mi`ad mialyd t"r .seqpi` mkxre miniiw lim x →∞ R x + b x e t 2 dt - e lim x →∞ R x + a x
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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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infi2HW03 - 3 A4 'qn milibxz oeilb - 104281 28 - 2 itpi`...

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