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Date: Wed, 29 Oct 2003 16:41:22 +0100 (CET)
Subject: Re: zadachki (dlja Mamy)
From: yurii@deds.nl
To: "Khomskii" <khomskii@ph2.uni-koeln.de>
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Vot zadachki:

1. Pokazat shto

           sin(x/n)
f(x) =  _____________
                    n
         (1 + (x/n))

v kazhdom x convergirujet na 0 (pomojemu na 0, esli net, to kuda?)


  I, shto eta-zhe functia, po modulju, integrirujetsja ot 0 do
bezkonechnosti (znachit Integral convergirujet)



2. Tozhe samoe dlja

                 2
          1 + n x
f(x) = _____________
                  n
          /     2\
          \1 + x /


    Wse eto na intervale 0 do 1, i integral tozhe ot 0 do 1




3. Tozhe samoje dlja



                n
f(x) =   _________________
                  2 2
             1 + n x


  I predely sdes ot a do bezkonechnosti (i integral, i convergentsia dlja
kazhdovo x > a). Podskazka govorit chto nado razlichat sluchayi a < 0, a
= 0 i a > 0.

Wot vrode poka wse.


-Yurii

PS. esli eti formuli ne poluchilis na washem computere, pobrobujte
polzovatsja drugoj programkoj, namrimer elm ili pine etc. Esli net to
napishite mne i ja escheraz napishu.