ko`rsatkichli funksiya va ko`rsatkichli tenglama ko'rsatkichli tengsizliklar

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ko`rsatkichli tengsizliklar ko`rsatkichli tengsizliklar. reja: 1. ko`rsatkichli funksiya 2. ko`rsatkichli tenglamalar 3. ko`rsatkichli tengsizliklar va ularni yechish usullari ko`rsatkichli funksiya darajaning ba`zi xossalarini eslatib o`tamiz. faraz qilaylik, a>0, b>0, bo`lib, m, n, k – haqiqiy sonlar bo`lsin. u holda , , , , , , , , ; , – tengliklar o`rinli bo`ladi. ta`rif: , ya`ni asosi o`zgarmas, daraja ko`rsatkichi o`zgaruv-chi bo`lgan funksiya, ko`rsatkichli funksiya deyiladi, bu yerda a- beryl-gan son bo`lib, a>0 va a ≠ 1 bu funksiyaning xossalarini ko`rib chiqamiz: 1. bu funksiya ning barcha qiymatlari uchun aniqlangan, ya`ni funksiyaning aniqlanish sohasi haqiqiy sonlar to`plamidan iborat. 2. -ning barcha qiymatlari uchun , chunki , . shu-ning uchun funksiyaning qiymatlar sohasi barcha musbat sonlar-dan iborat , ya`ni . 3. bo`lsin. a) bo`lganda, bo`ladi. haqiqatda, bu tengsizlikning ikkala tomonini ga bo`lamiz va ni yoki ni hosil qilamiz. shartga ko`ra va bo`lganidan bu tengsizlik-ning tog`riligiga ishonch hosil qilamiz: b) 0 1 …

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di. chap tomondagi tengsizlik barcha x uchun bajariladi, o`ng tomon esa ≤-1 bo`lganda bajariladi. javob: . 6. tengsizlikni yeching. yechish: ketma-ket quyidagicha o`zgartirib yozamiz: . ikkala tomonni ga ko`paytiramiz: hosil bo`ladi. yechim: . 7. tengsizlikni yeching. yechish: tengsizlikni ko`rinishida yozib, ni hosil qilamiz. bundan ( +4)( -3)>0 va 3 ni topamiz. javob: . mashqlar tengsizliklarni yeching. javoblar: 294. . 295. 2) 296. 2) ko`rsatkichli tenglamalar ko`p hollarda ko`rsatkichli tenglama ko`rinishga keltiriladi. bu yerda . bu tenglama yagona yechim ga ega, chunki quyidagi teorema o`rinli. teorema. agar va bo`lsa, tenglikdan ho-sil bo`ladi. isbot. faraz qilaylik, tenglik bajarilmasin, ya`ni yoki bo`lsin. u holda va bo`lganda funksiya o`suvchi-ligidan kelib chiqadi, bo`lganda esa, bo`ladi. ikkala holda ham shart bajarilmadi, demak farazimiz noto`g`ri va teorema isbotlandi. 1-misol. tenglamani yeching. yechish: tenglamani yoki shaklda yozamiz va ni hosil qilib, bundan ni topamiz. javob: . 2-misol. tenglamani yeching. yechish: va bo`lgani uchun, tenglamani yoki ko`rinishda yozib, ni …

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; 8) 5 ; 10) 4; 12 ; 14) 1; 16) 1; 18) 1; 20) , 3. ko`rsatkichli tengsizliklar va ularni yechish usullari ko`rsatkichli tengsizlik ko`p holatlarda ma`lum soddalashtirishlar-dan keyin yoki ko`rinishiga keltiriladi. bu tengsizliklar ko`rsatkichli funksiyaning o`suvchi yoki kamayuvchi xossasini hisobga olgan holda yechiladi: yoki misollar: 1. tengsizlikni yeching. yechish: asos 2>1 bo`lgani uchun dan ni hosil qila-miz. bundan esa yoki va hosil bo`ladi. javob: . 2. 2. tengsizlikni yeching. yechish. tengsizlikni ko`rinishida yozamiz va asos 0,5 -4 yoki hosil bo`ladi. javob: . 3. tengsizlik yechilsin. yechish: 3x=t deb qabul qilsak, 9x=32x=t2 bo`ladi va berilgan teng-sizlikka teng kuchli t2+t-2>0 tengsizlik hosil bo`ladi. uni (t-1)(t+2)>0 ko`rinishida yozib yechim t 1 ni hosil qilamiz. x o`zgaruvchiga o`tsak, 3x 1 ni hosil qilamiz. birinchi tengsizlik yechimga ega emas, chunki barcha haqiqiy uchun 3x>0. ikkinchi tengsizlikni 3x>30 ko`rinishida yozib, bundan x>0 ni hosil qilamiz. javob: . 4. tengsizlikni yeching. yechish: qavsdan ni chiqarib, …

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asoslari. 10-11 sinflar uchun darslik. toshkent, “o`qituvchi”, 1992-yil. 3. vafoyev r. h. va boshqalar. algebra va analiz asoslari. akademik litsey va kasb-hunar kollejlari uchun o`quv qo`llanma. toshkent, “o`qituvchi”, 2001-yil. 4. abduhamidov a. u. va boshqalar. algebra va analiz asoslari. akademik litsey va kasb-hunar kollejlari uchun sinov darsligi. toshkent, “o`qituvchi”, 2001 yil. 5. antonov k. p. va boshqalar. elementar matematika masalalari to`plami. toshkent, “o`qituvchi”, 1975-yil va keyingi nashrlari. 6. skanavi m. n. tahriri ostida. matematikadan masalalar to`plami. toshkent, “o`qituvchi”, 1983-yil va keyingi nashrlari. _1405259461.unknown _1405259525.unknown _1405259590.unknown _1405259614.unknown _1405259630.unknown _1405259646.unknown _1405259654.unknown _1405259658.unknown _1405259660.unknown _1405259662.unknown _1405259663.unknown _1405259664.unknown _1405259661.unknown _1405259659.unknown _1405259656.unknown _1405259657.unknown _1405259655.unknown _1405259650.unknown _1405259652.unknown _1405259653.unknown _1405259651.unknown _1405259648.unknown _1405259649.unknown _1405259647.unknown _1405259638.unknown _1405259642.unknown _1405259644.unknown _1405259645.unknown _1405259643.unknown _1405259640.unknown _1405259641.unknown _1405259639.unknown _1405259634.unknown _1405259636.unknown _1405259637.unknown _1405259635.unknown _1405259632.unknown _1405259633.unknown _1405259631.unknown _1405259622.unknown _1405259626.unknown _1405259628.unknown _1405259629.unknown _1405259627.unknown _1405259624.unknown _1405259625.unknown _1405259623.unknown _1405259618.unknown _1405259620.unknown _1405259621.unknown _1405259619.unknown _1405259616.unknown _1405259617.unknown _1405259615.unknown _1405259606.unknown _1405259610.unknown _1405259612.unknown _1405259613.unknown _1405259611.unknown _1405259608.unknown _1405259609.unknown _1405259607.unknown _1405259598.unknown _1405259602.unknown _1405259604.unknown _1405259605.unknown _1405259603.unknown _1405259600.unknown

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ko`rsatkichli tengsizliklar ko`rsatkichli tengsizliklar. reja: 1. ko`rsatkichli funksiya 2. ko`rsatkichli tenglamalar 3. ko`rsatkichli tengsizliklar va ularni yechish usullari ko`rsatkichli funksiya darajaning ba`zi xossalarini eslatib o`tamiz. faraz qilaylik, a>0, b>0, bo`lib, m, n, k – haqiqiy sonlar bo`lsin. u holda , , , , , , , , ; , – tengliklar o`rinli bo`ladi. ta`rif: , ya`ni asosi o`zgarmas, daraja ko`rsatkichi o`zgaruv-chi bo`lgan funksiya, ko`rsatkichli funksiya deyiladi, bu yerda a- beryl-gan son bo`lib, a>0 va a ≠ 1 bu funksiyaning xossalarini ko`rib chiqamiz: 1. bu funksiya ning barcha qiymatlari uchun aniqlangan, ya`ni funksiyaning aniqlanish sohasi haqiqiy sonlar to`plamidan iborat. 2. -ning barcha qiymatlari uchun , chunki , . shu-ning uchun funksiyaning qiymatlar sohasi b...

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