DARAJALI FUNKSIYA, UNING GRAFIGI VA TADBIQLARI

Authors

  • Raximova Gullola Shavkatovna Author

Keywords:

Kalit so‘zlar: Darajali funksiya, eksponent, monomial, algebra, funksiya grafigi, matematik analiz, iqtisodiy model, differensial, integral, limit, asimptotik xatti-harakat, vizualizatsiya, tadbiq.

Abstract

 
Annotatsiya:  Ushbu  maqola  asosiy  e’tiborni  darajali  funktsiyalarga,  ularning 
grafigi  va  keng  amaliy  tadbiqlariga  qaratadi.  Kichikdan  kattaga,  oddiydan 
murakkabga, abstrakt nazariyadan haqiqiy hayotiy sohalargacha darajali funksiyaning 
o‘rni chuqur tahlil qilinadi. Matnda alohida tarzda har bir ixtiyoriy darajali funksiya 
uchun analitik asos, xossalar va grafigi o‘rganiladi. Darajali funksiyalarning matematik 
va  vizual  tahlili,  ularni  kompleks  va  real  muammolarda  modellashtirishda  qanday 
foydalanish  mumkinligi  keng  yoritiladi.  Xususan,  darajali  funksiyaning  matematik 
mohiyati,  grafigi  tuzilishi,  har  xil  exponentlar  uchun  graf  oqimi  va  amaliy 
implementatsiyasi  haqida  batafsil  ma’lumot  keltiriladi.  Matn  davomida  fan-texnika 
taraqqiyotida  va  iqtisodiy,  texnik  hamda  statistik  modellashtirishda  darajali 
funksiyalarning qanday universal vosita ekani asoslanadi. 

References

Foydalanilgan adabiyotlar

1. Larson R., Edwards B., “Calculus”, 11th Edition, Cengage Learning, 2018.

2. Boyce W. E., DiPrima R. C., Meade D. B., “Elementary Differential Equations

and Boundary Value Problems”, 11th Edition, Wiley, 2017.

3. Stewart J., Clegg D., Watson S., “Calculus: Early Transcendentals”, 9th

Edition, Cengage Learning, 2020.

4. Papoulis A., Pillai S. U., “Probability, Random Variables, and Stochastic

Processes”, 4th Edition, McGraw-Hill, 2012.

5. Strang G., “Linear Algebra and Learning from Data”, Wellesley-Cambridge

Press, 2019.

6. Johnson R. A., Miller I., Freund J., “Probability and Statistics for Engineers”,

9th Edition, Pearson, 2016.

7. Thomas G. B., Weir M. D., Hass J., “Thomas' Calculus”, 14th Edition, Pearson,

2018.

8. Molchanov S., “Methods of Mathematical Physics”, Springer, 2022.

Published

2026-07-05

How to Cite

Raximova Gullola Shavkatovna. (2026). DARAJALI FUNKSIYA, UNING GRAFIGI VA TADBIQLARI . Ta’lim Innovatsiyasi Va Integratsiyasi, 72(1), 306-309. https://journalss.org/index.php/tal/article/view/35661