Кудрявцев Л.Д. Курс математического анализа. В 3-х томах. Том 1 (2003) (1095450), страница 16

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"* ' +' ( ' " "&")(&t)&t)J&t)*",&t)I&&t)&t)J&t))t∈<7 &<H=S/<SH4) / ( (( ((C"t∈J&t)I4( &t) &t)1 ' #&t)I&&t)&t)) ! QQ 6 ! '"@ ! & ) /LM(("( 6& :&%9 #< 6&4B$6?&t)t∈#tt4&<&6tIt4)%<j_s Q&t)UQI4&<H<)t → t4>& %<$#M$&j_s &t)I&<HF)t → t4'Q&t)UQ /(-!((&<H<)'&<HF)!εW4*δW4"t∈ f&t41δ)&<HP)Q&t)UQVε&<HR)0"(! t4 / & !) Ct4 /&<HP) QtUt4QVδt∈t4 /!"TU*"",<<<QtQW --δ- tW --δ- tVU --δ- t∈C " &t) &)&<HR)!"&t)t∈ f&t41δ)& <HP)) #ε& [R)C &t) I &&t) &t) J&t)) II&<FP)ε&t)U4&t)7[RQ&t)UQI [ ( t ) F < ] F T [ ( t ) F F ] F T [ J ( t ) F P ] F&<HH)Q&t)U<QQ&t)UQQ&t)UFQ+'Q&t)UQQJ&t)UPQQ&t)UQ&<HS)j_s &t)I&<H[)t → t4j_s &t)I< j_s &t)IF j_s J&t)IPt → t4t → t4t → t4&<H>) # &<HH) &<HS) !&<H<)!"!j_s Q&t)U<QI4 j_s Q&t)UFQI4 j_s QJ&t)UPQI4t → t4t → t4t → t4 /%<t4 /69&6&&1 1%<)<9B$6?&t)t∈ & %&%&j_s &t)I&t4)t → t4&<H=)&>&B$6?9:&%9#4&6t40 " ( &<H=) * j_s (t) t4 3 't → t4 &<H[) &<H>) ( ' (5&(+4< /%< j_s &t)I& j_s Q&t)QIQQt → t4t → t4QQQUQQQQUQA ' " #F4 j_s L<&t)TF&t)MI j_s <&t)T j_s F&t)4t → t4t → t4t → t4P j_s A&t) &t) I j_s A&t) j_s &t) &A&t) / %6<99t → t4t → t4t → t4t → t4t → t4B$6?9)4R j_s <&t) F&t)I j_s <&t) j_s F&t)4t → t4H j_s <&t)F&t)I j_s <&t)× j_s F&t)t → t444t → t4t → t4 " < /H ( 44 "F /H"** **""('!! ##& R=H<4) H4+!"QQIQQ QQ `_b 'QQ QQ&<H<4)+'I&t)I&t) j_s Q&t)QI4Q&t)Q /t → t4(&<H<4)& H<<)j_s QQI4t → t4&<H<<)+ j_s <&t)I j_s F&t)I+ &t)It → t4t → t4I <&t)Uβ&t)IF&t)U1&<H<)j_s Q&t)QI j_s Q&t)QI4t → t4t → t4<&t)F&t)ILTα&t)MLTβ&t)MIIT&t)T&t) T&t)&t)&<H<F)&<H<<)j_s Q&t)QI j_s Q&t)QI j_s Q&t)&t)QI4t → t4t → t4t → t4Q&t)T&t)T&t)&t)QQ&t)QTQ&t)QTQ&t)&t)Q j_s Qβ&t)Tα&t)Tα&t)β&t)QI4+'t → t4j_s Q<&t)F&t)UQI4t → t4'& <)j_s &t)F&t)It → t4 <4 H 5<4/H4"( *(&<HH)*" " ( " " "3 " ( "( "( ' % 938818 # * ( ! t4 / t4!+ ( &t) ( t ) F ( t4 )- t41# -----------------------------tFt4*'(t) F (t )t F t4t → t44 *< j_s ------------------------------- &%< [ 6[ %$(8%&$&) :&%9 #:4 4 6&4B$6?&6t42:&%9$&t4)<· &t4)1-!(C ∆tItUt4∆I&t4T∆t)U&t4)∆-′&t4)I j_s ----∆t&<H<P)∆t → t 4!(&t)I&&t)&t)J&t))t4t4!"!(&t)&t)J&t)tIt4'′&t4)I& ′&t4) ′&t4)J′&t4))Q′&t4)QI ( ′ ) F ( t 4 ) T ′F ( t 4 ) T J′F ( t 4 )  ' ""&<H[)&<H>)(, ( t F ∆t ) F ( t ) ( t T ∆t ) F ( t )4444- I  j_s ------------------------------------------------j_s ---------------------------------------------∆t∆t ∆t → 4 ( t 4 T ∆t ) F ( t 4 )J ( t 4 T ∆t ) F J ( t 4 )- j_s ----------------------------------------------- j_s -----------------------------------------------∆t∆t∆t → 4∆t → 4∆t → 4+′&t)(&t)%6%&;7: 9 6&&t)&%&<; #(&t&t)′&t) %6%&;78(9 &t) ! / %<: %6%&89+"(( &t) t ∈ 2%6 <4 &%(&<; %6<94 B$6?β&t)t∈t4#&t)I&β&t))t 4*(&t) (&t)β&t)"t It4&t)I&t) β&t)t∈ j_s &t)I4∆t → t 40"(t4∈(&t)t4'ε&t4)I4 ( t <44tT /!("+" ((((( ! 6&9 B$6?9&t)#<9 (6&4 6%&%& &6 t4 :&%9 BB?($ 4#tIt4%<#8∆I&t4T∆t)U&t4)&6t4#%& ∆I∆tT&∆t)∆t4&<H<R)+'(∆t*∆tBB?< 6&4B$6(?&t)t4!_ _I∆t-!∆I_T&∆t)∆t4&<H<H)9(&∆t)∆tI41 ,! ) &∆U∆t)Q∆tI4I4&∆t)Q∆tI4 ( <H<R@'(&∆t)&∆t)I&∆t)∆t(&∆t)! ∆tI4'&<H<S)j_s ε&∆t)I4∆t → 4 ∆tI41!#'ε&4)I43 &<H<R) ! ( &t) (( t4 '&<H<R)∆- I j_sj_s ----∆t∆t → 4∆t → 4 ( ∆t )- IT ------------∆t (&t)((t4'′&t4)I∆- ;!*′&t4)I j_s ----∆t → 4 ∆t∆- T&∆t)∆t4′&t4)I ----∆tj_s &∆t)I4&<H<[)∆I$&t4)∆tT&∆t)∆t&<H<>)∆t → 4∆t 4C ε&4) I 4 &<H<[)&<H<>)&<H<R) I ′&t4)-!(b&t)(( t4_&t4)I′&t4)∆t+ ' _t I ∆t &!)_I_I ′_t′I -----_t+tIt&τ) /((τIτ4(t4It&τ4)∆τIτUτ43#&<H<>)∆∆t∆t------ I t′ ------ Tε&∆t) ------ &<H<=)∆τ∆τ∆τ t′ I′&t4).

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