maxsus nuqtalar va ularning tiplari

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1576157789.doc ) ( z f w = 0 z ) ( z f z e z f = ) ( z e z f = ) ( ' z ) ( ' z f z e 1 1 ) ( 2 + = z z f i i - , ) ( z f w = 0 z 0 ) ( , 0 ) ( ... ) ( ' ' ) ( ' ) ( 0 ) ( 0 ) 1 ( 0 0 0 ¹ = = = = = - z f z f z f z f z f n n 0 z ) ( z f 1 = n 0 z 0 z ) ( ) ( ) ( 0 z z z z f n j - = ) ( z j 0 z 0 ) ( 0 ¹ z j 0 z ) ( …

= , x z = 2 1 ) ( z e x f = 0 ® x ¥ ® ) ( x f , iy z = o e iy f y ® = - 2 1 ) ( o y ® o z = 2 1 ) ( z e z f = o z = ... ! ... ! 2 1 2 + + + + + = n z z z e n z ... ! 1 ... ! 3 1 ! 2 1 1 1 2 6 4 2 1 2 + + + + + + = n z z n z z z e o z = 2 1 z e maxsus nuqtalar va ularning tiplari maxsus nuqtalar va ularning tiplari reja: 1. funksiya nollari 2. ajralgan maxsus nuqtalar va uning tiplari 3. qutulib bo`ladigan maxsus nuqta. 4. qutblar. 5. muhim maxsus nuqtalar. tayanch …

lgan maxsus nuqtasi dan iborat, chunki bu nuqtada berilgan funksiya hosilaga ega emas, lekin uning harqanday atrofida hosilada mavjud. ajralgan maxsus nuqtalar uch tipga ya`ni qutulib bo`ladigan (yoki chetlashtirilgan) maxsus nuqtalar, qutblar va muhim maxsus nuqtalarga bo`linadi. ta`rif. agar: a) bo`lib, a aniq chekli son bo`lsa, u holda nuqta funksiyaning qutulib bo`ladigan (yoki chetlashtiriladigan) maxsus nuqtasi; b) bo`lsa, u holda nuqta funksiyaning qutbi; c) mavjud bo`lmasa nuqta funksiyaning muhum maxsus deyiladi. agar funksiya ajralgan maxsus nuqtaga ega bo`lsa, uning qaysi tipga kirishini asosan usha funksiyaning loran qatoriga yoyilmasi yordami bilan aniqlanadi. 2.1. qutulib bo`ladigan maxsus nuqta. teorema. funksiyaning ajralgan maxsus nuqtasi qutulib bo`ladigan maxsus nuqtasi bo`lishining zaruriy va yetarli sharti shu funksiyaning nuqta atrofidagi loran qatoriga yoyilmasi bosh qisimga ega bo`lmasligidan iboratdir, ya`ni loran qatorining to`g`ri qismidir. misol. 1) funksiyada ajralgan maxsus nuqtaning tipini aniqlang. yechish. berilgan funksiyaning ajralgan maxsus nuqtasi dan iborat bo`lib, bo`lganda esa . demak, bu limit …

funksiyaning ajralgan maxsus nuqtasi qutb bo`lishi uchun funksiyaning nuqta atrofida loran qatori bosh qismi hadlarining soni chekli bo`lishi zarur va yetarlidir: , bunda misol. quyidagi funksiyalarning qutblari topilsin. a) b) yechish. a) funksiyaning oddiy noli, ya`ni funksiyaning oddiy qutbi. b) funksiya nuqtada aniq emas, chunki buni aniqlash uchun ni qatorga yoyamiz: embed equation.3 bunda limitga o`tsak , ya`ni qutulib bo`ladigan maxsus nuqta. endi boshqa maxsus nuqtalarni ham topish uchun kasr maxrajining nollarini aniqlaymiz: . bizga ma`lumki . demak, nuqtalar berilgan funksiyaning oddiy qutblaridir. 2.3 muhim maxsus nuqtalar. biz muhim maxsus nuqta uchun o`rinli bo`lgan teoremani qaraymiz. teorema. funksiyaning ajralgan maxsus nuqtasi muhim maxsus nuqtadan iborat bo`lishi uchun shu funksiyaning nuqta atrofidagi loran qatorining bosh qismi cheksiz ko`p hadlarga ega bo`lishi zarur va yetarlidir: xususiy holda loran qatorining to`g`ri qismi bo`lmasligi ham mumkin, ya`ni biroq ,…, bo`lishi mutlaqo shart. misol. funksiyaning maxsus nuqtalari va uning tafsifi aniqlansin. yechish. 1-usul maxsus nuqta. …

. “tеoriya vеroyatnostеy i matеmatichеskaya statistika” .m: vo`sshaya shkola, 1990g. 7. gmurman v.е. “ehtimollar nazariyasi va matеmatik statistika”, toshkеnt, o`qituvchi, 1978y. 8. s. sirojdinnov , m.mamatov. “ehtimollar nazariyasi va matеmatik statistika”. toshkеnt., “o`qituvchi”. 1982y. 9. gmurman v.е. “ehtimollar nazariyasi va matеmatik statistika”dan masalalar yеchishga doir qo`llanma, toshkеnt., “o`qituvchi”, 1980y. _1326644273.unknown _1326646852.unknown _1326647377.unknown _1326835920.unknown _1326836139.unknown _1326836439.unknown _1326836466.unknown _1326836690.unknown _1326836860.unknown _1326836458.unknown _1326836296.unknown _1326836309.unknown _1326836180.unknown _1326836096.unknown _1326836121.unknown _1326836054.unknown _1326647904.unknown _1326648838.unknown _1326649129.unknown _1326648980.unknown _1326647940.unknown _1326647632.unknown _1326647681.unknown _1326647461.unknown _1326647156.unknown _1326647308.unknown _1326647362.unknown _1326647241.unknown _1326646982.unknown _1326647109.unknown _1326646897.unknown _1326645526.unknown _1326646342.unknown _1326646585.unknown _1326646818.unknown _1326646441.unknown _1326645814.unknown _1326645859.unknown _1326645715.unknown _1326644880.unknown _1326645025.unknown _1326645308.unknown _1326644985.unknown _1326644792.unknown _1326644841.unknown _1326644757.unknown _1326640843.unknown _1326641730.unknown _1326642254.unknown _1326643794.unknown _1326644080.unknown _1326643990.unknown _1326644012.unknown _1326643651.unknown _1326642107.unknown _1326642179.unknown _1326641915.unknown _1326641253.unknown _1326641479.unknown _1326641623.unknown _1326641360.unknown _1326641204.unknown _1326641239.unknown _1326641095.unknown _1326641134.unknown _1326640929.unknown _1326617935.unknown _1326638116.unknown _1326640124.unknown _1326640445.unknown _1326640472.unknown _1326640271.unknown _1326638380.unknown _1326638493.unknown _1326638224.unknown _1326638254.unknown _1326619471.unknown _1326637444.unknown _1326637755.un

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1576157789.doc ) ( z f w = 0 z ) ( z f z e z f = ) ( z e z f = ) ( ' z ) ( ' z f z e 1 1 ) ( 2 + = z z f i i - , ) ( z f w = 0 z 0 ) ( , 0 ) ( ... ) ( ' ' ) ( ' ) ( 0 ) ( 0 ) 1 ( 0 0 0 ¹ = = = = = - z f z f z f z f z f n n 0 z ) ( z f 1 = n 0 z 0 z ) ( ) …

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