infi2HW08 - dtivx f ( x ) m`y jkn ewiqd . n lkl lim x...

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8 'qn milibxz oeilb - 104281 - 2 itpi` .mixdva 12 : 00 dry cr -- 2008 uxnl 13 :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 y miiwzn n lk xear m` ik e`xd . f ( x ) divwpetl [0 , ) - a y"na zeqpkzn f n ( x ) ik oezp .` . lim x →∞ f ( x ) = 0 miiwzn mb if` lim x →∞ f n ( x ) = 0 .dwitqn dpi` zizcewp zeqpkzdy d`xnd `nbec epz .a 2 libxz :onqp . I = [0 , ) - a dtivx f ( x ) g n ( x ) = n Z x + 1 n x f ( t ) dt :egiked . I - a f ( x ) l zizcewp zeqpkzn g n ( x ) .1 . I - a f ( x ) l y"na zeqpkzn g n ( x ) ik e`xd .y"na dtivx f ( x ) y sqepa oezp .2 zixyt` jxc) . [0 , ) - a y"na `l j` zizcewp zeqpkzn g n ( x ) y jk f ( x ) - l `nbec epz .3 (.`ad sirqa riten y"na dpi` zeqpkzddy ze`xdl zg`
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Unformatted text preview: dtivx f ( x ) m`y jkn ewiqd . n lkl lim x →∞ g n ( x ) = 0 ik e`xd .qpkzn R ∞ f ( x ) dx oezp .4 . lim x →∞ f ( x ) = 0 if` y"na 3 libxz dpi` j` meqg rhw lka y"na zqpkzn dxcqdy e`xd . f n ( x ) = ‡ 1-x 2 n · n dxcqd dpezp .iynnd xyid lk lr y"na zqpkzn 4 libxz :onqp h n ( x ) = nx 1 + e nx g n ( x ) = x n (1 + e x/n )- a zeqpkzdd m`d .zizcewp (odizy) zeqpkzn g n ( x )- e h n ( x ) ea ilnqwnd I rhwd z` e`vn zeivwpetd zxcq m`d ?y"na I k n ( x ) = h n ( x ) g n ( x ) ? I- a y"na zqpkzn 1...
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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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