tekis uzluksizlik

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o‘zmu matematik analiz kafedrasi 17-ma’ruza tekis uzluksizlik reja 1. funksiyaning tekis uzluksizligi tushunchasi. 2. kantor teoremasi. adabiyotlar 1. tao t. analysis 1. hindustan book agency, india, 2014. 2. xudayberganov g., vorisov a. k., mansurov x. t., shoimqulov b. a. matematik analizdan ma’ruzalar, i q. t. “voris-nashriyot”, 2010. 3. fixtengolts g. m. kurs differentsialnogo i integralnogo ischisleniya, 1 t. m. «fizmatlit», 2001. 1. funksiyaning tekis uzluksizligi tushunchasi. faraz qilaylik funksiya to‘plamda berilgan bo‘lsin. 1-ta’rif. ([1], p. 244, def. 9.9.2) agar ixtiyoriy son olinganda ham shunday son topilsaki, tengsizlikni qanoatlantiruvchi ixtiyoriy uchun tengsizlik bajarilsa, ya’ni bo‘lsa, funksiya to‘plamda tekis uzluksiz deyiladi. keltirilgan ta’rifdan: 1) sonning faqat ga bog‘liqligi, 2) funksiya da tekis uzluksiz bo‘lsa, y shu to‘plamda uzluksiz bo‘lishi kelib chiqadi. 1-misol. bo‘lsin. bu funksiya da tekis uzluksiz bo‘ladi. ◄ agar ga ko‘ra deb olinsa, unda da bo‘ladi. ► 2-misol. bo‘lsin. bu funksiya da tekis uzluksiz bo‘ladi. ◄ agar ga ko‘ra, deyilsa, …

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uchun deb olingan farazga zid. demak funksiya da tekis uzluksiz. ► 2-ta’rif. faraz qilaylik funksiya to‘plamda berilgan bo‘lsin. ushbu ayirma funksiyaning to‘plamdagi tebranishi deyiladi va u opqali belgilanadi: . funksiyaning to‘plamdagi tebpanishi qyyidagicha ham ta’riflanishi mumkin. natija. agar bo‘lsa, u holda uchun shunday topiladiki, segment uzunliklari dan kichik bo‘laklarga ajratilganda har bir bo‘lakdagi funksiyaning tebranishi dan kichik bo‘ladi. ◄ shartga ko‘ra . demak, kantor teoremasiga ko‘ra u da tekis uzluksiz. unda ta’rifga binoan bo‘ladi. endi segmentni uzunligi dan kichik bo‘lgan bo‘laklarga ajaratamiz. unda bo‘ladi. demak, bo‘ladi. ► funksiyaning uzluksizlik moduli. funksiya to‘plamda berilgan bo‘lib, u shu to‘plamda uzluksiz bo‘lsin. endi uchun (1) ayirmani qaraymiz. 3-ta’rif. (1) ayirmaning aniq yuqori chegarasi funksiyaning to‘plamdagi uzluksizlik moduli deyiladi va kabi belgilanadi: . demak, funksiyaning to‘plamdagi uzluksizlik moduli ning manfiy bo‘lmagan funksiyasi bo‘ladi. endi uzluksizlik modulining ba’zi xossalarini keltiramiz: 1) funksiyaning uzluksizlik moduli ning o‘suvchi funksiyasi bo‘ladi. ◄ aytaylik, va bo‘lsin. u holda , …

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bu (bunda , ) tengsizlikni qanoatlantiruvchi funksiualar to‘plami tartibli lipshits sinfi deyiladi va kabi belgilanadi. mashqlar 1. agar va funksiyalapning har biri da tekis uzluksiz bo‘lsa, u holda ( funksiya ham da tekis uzluksiz bo‘lishi isbotlansin. 2. funksiyaning da tekis uzluksiz emasligi ko‘rsatilsin. 3. ushbu funksiyaning segmentdagi uzluksizlik moduli topilsin. 4. agar funksiya (0,1) da tekis uzluksiz bo‘lsa, ushbu limit mavjud bo‘ladimi? nazorat savollari 1. funksiyaning tekis uzluksizlugi. 2. kantor teoremasi. 3. funksiyaning to‘plamdagi tebranishi nima? 4. funksiyaning to‘plamdagi uzluksizlik moduli nima? 1 _1265225733.unknown _1265226280.unknown _1522134348.unknown _1522134514.unknown _1522134798.unknown _1522483648.unknown _1523167465.unknown _1523167506.unknown _1523167524.unknown _1523167845.unknown _1523167477.unknown _1522483681.unknown _1522483785.unknown _1522483809.unknown _1522483692.unknown _1522483658.unknown _1522134829.unknown _1522134856.unknown _1522134959.unknown _1522134967.unknown _1522134889.unknown _1522134849.unknown _1522134808.unknown _1522134609.unknown _1522134781.unknown _1522134790.unknown _1522134655.unknown _1522134585.unknown _1522134600.unknown _1522134553.unknown _1522134386.unknown _1522134458.unknown _1522134462.unknown _1522134425.unknown _1522134364.unknown _1522134381.unknown _1522134358.unknown _1265226458.unknown _1265226582.unknown _1265226651.unknown _1265226708.unknown _1265226793.unknown _1522134239.unknown _1522134317.unknown _1272614851.unknown _1265226800.unknown _1265226732.unknown _1265226784.unknown _1265226713.unknown _1265226674.unknown _1265226683.unknown _1265226670.unknown _1265226630.unknown _1265226640.unknown _1265226599.unknown _1265226496.unknown _1265226511.unknown _1265226551.unknown _1265226503.unknown _1265226478.unknown _1265226484.unknown _1265226465.unknown _1265226325.unknown _1265226430.unknown _1265226441.unknown _1265226390.unknown _1265226295.unknown …

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unknown _1265226005.unknown _1265226135.unknown _1265226169.unknown _1265226216.unknown _1265226261.unknown _1265226176.unknown _1265226150.unknown _1265226156.unknown _1265226139.unknown _1265226039.unknown _1265226055.unknown _1265226124.unknown _1265226048.unknown _1265226020.unknown _1265226025.unknown _1265226016.unknown _1265225840.unknown _1265225890.unknown _1265225946.unknown _1265226001.unknown _1265225941.unknown _1265225870.unknown _1265225878.unknown _1265225862.unknown _1265225771.unknown _1265225794.unknown _1265225830.unknown _1265225781.unknown _1265225745.unknown _1265225764.unknown _1265225737.unknown _1265225412.unknown _1265225593.unknown _1265225677.unknown _1265225704.unknown _1265225717.unknown _1265225722.unknown _1265225712.unknown _1265225686.unknown _1265225696.unknown _1265225681.unknown _1265225651.unknown _1265225668.unknown _1265225672.unknown _1265225656.unknown _1265225629.unknown _1265225643.unknown _1265225610.unknown _1265225483.unknown _1265225519.unknown _1265225554.unknown _1265225566.unknown _1265225549.unknown _1265225492.unknown _1265225503.unknown _1265225487.unknown _1265225447.unknown _1265225471.unknown _1265225476.unknown _1265225466.unknown _1265225426.unknown _1265225433.unknown _1265225420.unknown _1265205198.unknown _1265205447.unknown _1265205594.unknown _1265205597.unknown _1265205598.unknown _1265205595.unknown _1265205502.unknown _1265205591.unknown _1265205592.unknown _1265205508.unknown _1265205590.unknown _1265205495.unknown _1265205360.unknown _1265205420.unknown _1265205426.unknown _1265205414.unknown _1265205341.unknown _1265205350.unknown _1265205328.unknown _1265205219.unknown _1265205230.unknown _1265205135.unknown _1265205160.unknown _1265205177.unknown _1265205189.unknown _1265205172.unknown _1265205147.unknown _1265205153.unknown _1265205140.unknown _1265205111.unknown _1265205124.unknown _1265205128.unknown _1265205117.unknown _1265204648.unknown _1265204655.unknown _1265204640.unknown _1064862394.

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unknown ) ( x f r x ì 0 > e 0 > d d $ > " x x x x x e d 0 > e ) ( x f x x r x x x f î = , ) ( r 0 > " e e d = d " e e d = d " e 2 1 = e ' x ' ' x 1 x n ¢ = 1 1 x n ¢¢ = + () nn î | ' ' ' | x x - ) 1 ( 1 1 1 1 | | + = + - = ¢ ¢ - ¢ n n n n x x (|'''|) xx d - = + - = ¢ ¢ - ¢ = ¢ ¢ - 2 1 1 | ) 1 ( | 1 1 | ) ( ) ' ( | …

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o‘zmu matematik analiz kafedrasi 17-ma’ruza tekis uzluksizlik reja 1. funksiyaning tekis uzluksizligi tushunchasi. 2. kantor teoremasi. adabiyotlar 1. tao t. analysis 1. hindustan book agency, india, 2014. 2. xudayberganov g., vorisov a. k., mansurov x. t., shoimqulov b. a. matematik analizdan ma’ruzalar, i q. t. “voris-nashriyot”, 2010. 3. fixtengolts g. m. kurs differentsialnogo i integralnogo ischisleniya, 1 t. m. «fizmatlit», 2001. 1. funksiyaning tekis uzluksizligi tushunchasi. faraz qilaylik funksiya to‘plamda berilgan bo‘lsin. 1-ta’rif. ([1], p. 244, def. 9.9.2) agar ixtiyoriy son olinganda ham shunday son topilsaki, tengsizlikni qanoatlantiruvchi ixtiyoriy uchun tengsizlik bajarilsa, ya’ni bo‘lsa, funksiya to‘plamda tekis uzluksiz deyiladi. keltirilgan ta’rifdan: 1) sonning faqat g...

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