ikkinchi ajoyib limit va e soni

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1460113562_62069.pptx ikkinchi ajoyib limit va « e » soni ikkinchi ajoyib limit va « e » soni quyidagi  n x ketma –ketlikni qaraylik, ya’ni: , 1 1 n n n x          nn,1 (1) agar ,1n ,2n,3n bo’lsa,   , 1 1,, 3 1 1, 2 1 1,11 32 1 n n                      . (2) (2) ketma –ketlikning yaqinlashishini ko’rsatamiz. buning uchun  n x ketma –ketlikning o’suvchi va yuqoridan chegaralanganligini ko’rsatish yetarlidir. (1) ketma –ketlik uchun nyuton bin omi formulasini qo’llaymiz. u holda:    . 1 ! ]1[211 !2 11 1 2 n n nn nnnnn n nn n nx        bundan . 1 1 2 1 1 1 ! 1 …

e » soni 71828,2 ga teng bo’lib, u irrasional sondir. (7) ni quyidagi ko’rinishda ham yozish mumkin: 71828,2 1 1lim          e n n n . (9) misollar 1-misol. x x x         1 1lim limitni hisoblang. yechish: . 2 1 1lim 2 1 1lim 2 1 1lim 1 1lim 2 2 2 2 22 2 e xxx x x x x x x x x x                                                                     …

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1460113562_62069.pptx ikkinchi ajoyib limit va « e » soni ikkinchi ajoyib limit va « e » soni quyidagi  n x ketma –ketlikni qaraylik, ya’ni: , 1 1 n n n x          nn,1 (1) agar ,1n ,2n,3n bo’lsa,   , 1 1,, 3 1 1, 2 1 1,11 32 1 n n                      . (2) (2) ketma –ketlikning yaqinlashishini ko’rsatamiz. buning uchun  n x ketma –ketlikning o’suvchi va yuqoridan chegaralanganligini ko’rsatish yetarlidir. (1) ketma –ketlik uchun nyuton bin omi formulasini qo’llaymiz. u holda:    . 1 ! …

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