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Feb2007 - ANAAYEH I XHMMY OeBpoufiproq(Io61'roq 2007 B...

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ANAAYEH I. XHMMY * OeBpoufiproq (Io61'roq) 2007* B TIPOBAHMA 1 Ie 6l"o ro llp6Blqpo l, oe rcdOe npoypottrcrl o"uvdpqorl x -+.F(x) ovrtotorlof ps rrlv Fr,(x): f0) (1 + /. cosr), 6nots )"rupaypanr6q, 0<2<1. Itu eprrltqpora, f,A,E 06toupe F(x) : (l +x2)-1. A) No pe)"eqOe[ 11 o16oq avdpeoo oro ne6io opropori rT$ F rcsr cut6 n]C Fi. ro0rbq rcot ovdpeoo orrg pi(eg rnq F Kcrr ttq pi(eg qg Frr. Na Serltei 6tr q F1 eivot dpno 'fi nepwdl ov Kot p6vo ov ro i6ro ropier Tro rnv F. Yzro06rovrc,g 6tr ro zre6io optoprof A rnq F neprtllet 6vu 8rdoolpa pqrouq 2n, v0, unol"oytorei to el"dpoto &vco qpoYtlo (supremum) tou lrt") - F^G)ltlr61l yLa x e A. fro 7ro1o r rop5er F{x) = F(x); B) No 8etltei 6nq fi eivor avo).unrcr1 oe wa 6dotqpo,, o,v rcar p6vo av q F eivor eniorlg ovo)"utrrr1 oto i6ro 8tdorqpo. f) Ofroupe F(x): (1+x2)-r. Zqreiratq nupdyouoo ouvdprqoq G(x) = f,rg1at Ko,t ro epBo66v 2E tou lcrrpiou -13<1, 0<y<F(x). A) (F, G, E 6ncoq oro f): Nu ppeOofv ra o,vo,nnlylroro, o'e 8uvopooerpd rcor to orprBrl Draorripoto ol16l"roqq,pe r6vtpo ro x:0, rcDV ouvopn'loeov F rot G. Xprlorpozrotcovtoq to
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