Infi2_hw6 - 6 oeilib-2007 aia`(104281 2 itpi` 20 00 18 7...

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Unformatted text preview: 6 oeilib -2007 aia` - (104281) 2 itpi` 20 : 00 , 18 . 7 . 2007 ,iriax mei :dybd jix`z f : `dze , E ⊆ R dveaw lr zexcbend zeiynn zeivwpet zxcq { f n } ∞ n =1 `dz .1 yi m` wxe m` f l y'"na zqpkzn `l { f n } ∞ n =1 dxcqdy egiked . E → R mixtqn zxcqe , { n k } ∞ k =1 miirah mixtqn ly ynn dler dxcq zz , > . k lkl | f n k ( x n k )- f ( x n k ) | ≥ y jk E a zlkend { x n k } ∞ k =1 dcina `id zeqpkzdd m`d reawle ,mi`ad mixwna zeqpkzdd megz z` `evnl .2 :( x ∈ R f` zxg` xn`p `l m`) deey . f n ( x ) = sin( πe nx ) (`) . f n ( x ) = x cos( x/n ) (a) . x ∈ [0 , 1] xy`k f n ( x ) = 1 + x n n (b) . ∞ X n =2 1 n (ln( n )) x (c) .(? u n ( x ) = x n (1 + nx 2 ) ly meniqwnd edn :fnx) ∞ X n =1 x n (1 + nx 2 ) (d) :mi`ad zeleabd z` aygl .3 xy`k [ a, 3 π/ 4] rhwa zeqpkzdd ite` z` ewca :fnx) . lim n →∞ Z 3 π 4 cos n ( x ) dx (`) (ohw witqn a egwe , a > . lim x → ∑ ∞ k =1 k 2 k sin( x k ) ∑ ∞ k =1 k 3 k sin( x k ) (a) zeivwpetd zxcq z` mixicbn .dneqge dler zipehepen f 1 : [0...
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This note was uploaded on 06/27/2008 for the course MATH Infi 2 taught by Professor Benyamini during the Spring '08 term at Technion.

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Infi2_hw6 - 6 oeilib-2007 aia`(104281 2 itpi` 20 00 18 7...

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