# tutorial solution [13288] sequence of function.pdf - .sn...

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- squencedfuudndqcoslnilxl.sn Crnx ) fn Coscn ū x ) t.powtwise-cwwgso-nzfniU-IRqueuetfunctafn-nfpomhise.ly fw wg ZEU fncz ) = fy " fn ) = an " , [ 0,17 pick Z E [ 0,1 ) , Z < 1 fnlt ) = I % E = 0 = f
2. unifanconvwgmce.fm F 70 , NEN 1 ftc.f.cz , _ , .io iii ii. _ _ Efnfco fn.fi -.-
Supremum Norm llfll suplfslxEUlimsupffnczs-fczsllZEUJ-on-o-o-e.tt Unifam anvegmce -_- 7 pomtwise anvegeuce Mn = Sup { lfn-fljlfn-flLMnfilfn-f.io
ou T 0,1 ) : poutwise couvwguue f = o , Ixn -01 = lxnl i = nx " = o xcheck end powt : X 0 i X " = 0 lfx E [ 0,17 X " > o X < ( { lfn.fi J = 1 to Not unifwm aouvwge
2. fn = T.ge [ 0.0-99 ] X < 1 1 t ⼀⼀ ⼀点 f = 0 flfn f I = | iln ( 1 + == oltxn nx " = o X = oend pout test : fnlo ) = ofn ( 0 . 9 9 ) = - 1 + o . 9 9 "
l. -01 < - ' lto.qqnf.in = o = > fnisunifancowgace-nx23.fi = nxe T.l.es/.pomtwiselmif.onGi,Njhonxe-2=lim.nxn-gl'hnptd mle.no enx2-fY.xz.io Penxz
2. unifwmly anvwgmce gncx ) nx ē X > gn decreasing . 1 0--7 _ < o . 1 ti n_n when < ocl max.oflgcxsl-o.in e -0 -_- " gn-gllio.is = fyo.in e -0 " " = 0 we h ǎ e uuifwn anugmce
fn = nt onio.IS 4 tn 25 出品 fn - o = f lfn -01 = | 2 -0 | = | ˋ fii Elil -_- " ⼆年 4ntix2-zn3x214.in 22212 = 0 = ) 4 n = n 3 x 2 F = x -0
f = 3 f ou E ( " = > " memsnnfn.ly couvage ) 出品 llfn f 1 1 E = 0 K suchthd nsk Hffll Etl Thm UXEE.nsklfv.IE llfnll E 11 fn-ftftf-fkellfn-fHE-llflll-lf-fkHEE2tMKUM-ma.CM , -.- Mkn , 2 t Mk ) thm f nck , XEE we hd lfn K Mn EM And G nxk , XEE lfnlt 2 Mk f.is bounded su E
llcfn-igns-iftgllEElfn-f.NEtkgn-gHE-sasn-soo-ii.li Cfign ) - iftg HE 0 IMN fromlastpage.weknowxlfukM.lgnlt.NU n.andxEEThmlfl-fiylfnlEM.V-xc-E.ME