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funksional analiz misol va masalalar yechish 1 qism
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= max x ∈[0, 1] |f(x)|, lim n →∞ k (k − 1) 2n = 1. 2 ! lim n →∞ 1 n n =1 f (x ) = $ 1 0 f (x)dx. \ {x n } " [0, 1] $9 (+0+ 0- / 5 5 !5 5 & 5 5 ' 5 !5 5 . 5 5 5 !5 5 / 5 5 !5 5 α ∈ (0, 2) α ≥ 2 5 5 α ∈ (0, 2) α ≥ 2 f (x) = x α , α > 1 & 1 ' f (x) = √ x. . 5 , 5 #a#8" % f (x) = a ± x, x ∈ R. & R 2 ( f (x 1 , x 2 ) = (x 1 cos ϕ − x 2 sin ϕ + a 1 , x 1 sin ϕ + x 2 cos ϕ + a 2 ) g (x 1 , x 2 ) = (x 2 , x 1 ) $' 5 5 _ %9 @2 0 " - ' ' a < 1. 5 x = 1, 414 5 x = 3, 321 !5 x = −2, 369 % 2 . λ ∈ (−q, q), 0 < q < 1. λ ∈ (0, 1). &9 "0 ,+ 0 0 $ A & & ! ε > 0 A ε ! ε + B ⊂ A ! A ε & B ! ! ε #8#" & B & & % X = R, A = [0, 1] , B = (0, 1) . & #8a" ' 5 ε = 0, 5 5 ε = 1 2n . ε = √ 2 2 / 1 b M 1 (2, 1), M 2 (2, 3), M 3 (4, 1) M 4 (4, 3) & & A ! ε = √ 2 3#8#" ! 5 ")"# X = R, M = (0, 1), f(x) = 1 x X = R 2 , M = {(x, y) : y = 0} , F = (x, y) : x > 0, y = x −1 M y = x ! F & y = x ! $ ' + 5 5 5 ! " . C (1) [a, b] K & & ! ! + / M 2 , M 3 , M 4 . lim n →∞ a n = 0. 0 "4- " 5 * #"* %"* `"' b"d a"d 7"' 8"* W"d $"d #>"* ##"* #%"d #`"d #b"\ #a"\ #7"* #8"\ #W"* #$"* %>"' %#"' %%"\ %`"* %b"' %a"' %7"\ %8"d %W"* %$"* `>"* `#"\ `%"' ``"d `b"* `a"' `7"\ `8"* `W"' `$"d b>"* 1 ) -4- ) # hFRMFiFGFT jk lFMHB Dm nROMOBNo NOFGHH pQBIqHr H pQBIqH" BARBFiF ABARHJA SFPITA- kA QI A #$W$ % 2 1* ! 1 - #$$b ` 2 1* 1 - . ! #$W7 b stPNOGBHI s* DFEFROT mu nROMOBNo pQBIqHFBARvBFiF ABARHJA SFPITA- kA QI A #$7a a mj wGOBFiHB xS UHPAGOTPIHr w D DFEFROTA yAKA @H H QLGAz" BOBH{ LF pQBIqHFBARvBFMQ ABARHJQ SFPITA- kA QI A #$Wb 7 * & 2 * = == " . 0 ' %>>$ 8 X * Z0 Y+ 2 . [ . 1 "2 %>>$ W |HRHB mu SQMHBFT hh SONGH@OPIHO LGFPNGABPNTA w A}I OBN %>#> $ jx jBNFBOTH@ Uk hB{JFT ~m AKoBF yAKA @H H QLGAzBOBH{ LF pQBIqHFBARvBFMQ ABARHJQ SHBPI moP}A{ }I FRA #$8W #> FGF KOqIHr mm kAiBHEHKA ku kAPN APHOT UU SONF Ko GO}OBH{ JAKA @ LF pQBIqHFBARvBFMQ ABARHJQ hHOT #$$> ## CS xOGOJABPIHr l P y OpNORv lQBIqHFBARvBor ABARHJ hHOT- moVA{ }I FRA #$$> #% ?@AB CD DEFGBHI JAKA @ LF MANOMANH@OPI FMQ ABARHJQ " SFPITA UGFPTOVOBHO #$W# - 5 = ` ./d . / 1. /* /*Z 7 #" 1 & 1 & 7 %" * #8 `" 1 & %a b" 1 & `8 a" . ! & b8 ! + W# /['[Y 01[YZ*/ $% 7" . ! $% 8" d ! & / #>W W" / #%8 $" ! #`7 #>" * / "2 #ab ! + #8` [1Z= *./*Z #W% ##" #W% #%" _ ! " #$# #`" .! & & #$b #b" 1 %># #a" , %#a #7" < && %%7 #8" & & %`` ! + %b8 %ab B-0 4 *# ;C( !6 A ! ? ) "*# 68 @; A = ) "*# < =? B !6 1(= 8= = > D * ) "# : @8 - + Z - 0 ' 2 ! - 2 + - ' 1 0 * 0 #$> #>>a%>##" ' #b#>%>#a" < ! 7>Wb # #7 0 #7 > 2 #a 8a 2 `# #W * a>> ' 0 `#"#W )1 * *==,Z '.21.0) 1 _ $"#` )1 * *==,Z '.21.0) d X ! & 1 d ! #" Download 1.57 Mb. Do'stlaringiz bilan baham: 
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