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Lesson_14 - 'n1 ilxbhpi`e il`ivpxtic oeayg(104010 14 lebxz...

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Unformatted text preview: 'n1 ilxbhpi`e il`ivpxtic oeayg (104010) 14 lebxz oxia xnr :dkixr cwy inrp .xc ,ipinipa a`ei .text :ddbd uixw di`n :dqtcd zeivwpet ly zexcq ly deey dcina zeqpkzd 1 1 dxcbd m` I rhwa f ( x ) divwpetl deey dcina zqpkzn dxcqdy xn`p .zeivwpet zxcq { f n ( x ) } `dz :miiwzn x ∈ I lkle n > N lkly jk N yi ε > lkl | f n ( x )- f ( x ) | < ε :xaqd f n ( x ) zeivwpetd ly mitxbd eay ote`d z` yibcdl ick deey dcina zeqpkzdd z` mipkn ep` . f ( x ) ly sxbl miaxwzn j` lim n →∞ f n ( x ) = f ( x ) miiwzn x ∈ I lkl f` ,deey dcina f- l zqpkzn f n dxcqd m` . x-a dielz dppi`e ε-a wx dielz N zxigay `ed deey dcina zeqpkzda cgeind 1 libxz [ α, ∞ ) oxwa f ( x ) ≡ 1 divwpetl deey dcina zqpkzn f n ( x ) = nx 1 + nx zeivwpetd zxcqy gikep . α > lkl :oexzt . ε > `die , α > rawp :miiwzn x ∈ [ α, ∞ ) lkle n > N lkly jk N miiw :l"v | f n ( x )- f ( x ) | < ε 1 | f n ( x )- f ( x ) | = nx 1 + nx- 1 = nx- 1- nx 1 + nx = ( x> 0) 1 1 + nx ≤ ( x ≥ α> 0) 1 1 + nα < 1 nα < ε ⇐⇒ 1 εα < n . N = 1 εα + 1 xgap ,okl :zexrd . x-a ielz `l ep`vny N ok`y al miyp .1 :i"r dze` aygl yie , f ( x ) zileabd divwpetd idn y`xn mircei eppi` llk jxca .2 ∀ x ∈ I f ( x ) = lim n →∞ f n ( x ) :miiwzn eply `nbeca ,ok`e ∀ x ∈ [ α, ∞ ) f ( x ) = lim n →∞ f n ( x ) = lim n →∞ nx 1 + nx = 1 . f ( x ) ≡ 1 `id leab zeidl "zcnrend" ,xnelk 1 htyn .dtivx divwpetl zqpkzn ,y"na zqpkznd zetivx zeivwpet zxcq divwpetl I-a deey dcina zqpkzn dxcqde , I rhwa zetivx zeivwpet zxcq { f n } m` ,xnelk . I-a dtivx divwpet `id f...
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Lesson_14 - 'n1 ilxbhpi`e il`ivpxtic oeayg(104010 14 lebxz...

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