Math Problem Statement

6. Знайти границі функцій за допомогою правила Лопіталя; 7. Записати формулу Маклорена; 8. Дослідити функції та побудувати їх графіки; 9. Знайти розміри прямокутника з найбільшою площею; 10. Оцінка витрат на експлуатацію автомобіля.

Solution

It looks like you've uploaded an image containing several mathematical problems. I'll analyze and solve them step by step. Let me begin by addressing each question in order.from PIL import Image import pytesseract

Load the uploaded image

image_path = "/mnt/data/17324942084890gy1sf9p.jpg" image = Image.open(image_path)

Use OCR to extract text from the image

extracted_text = pytesseract.image_to_string(image, lang="ukr+eng")

Display the extracted text for review

extracted_text'6.31\n\nHira rpm dyusniit aa AouOMOroI Mpaniura Touivaas\n\nws\n5) lim () :\n\n1 bynsuil fe) = xsin a aanucarn dbopayay Maxanpena apyroro nopaye\nky it anammxonnst sienos y dopsti Tarpana\n\nsing— 2?\n\ni): ey oe\n\n8. ocaiuiim ynxnit ra no6yaynann ix rpadpixn\n\nztl é x\ney v=T\n\naly inet\n\n9. Y ypuxytimgy jomxnio0 oenonn & qHoMta FocrpHAKT KyTANH NPA OCHOR\ni micoto A saucano opawoxy rink vax, 10 JH Horo Hep porTAMOnasi HA\n\nOchoa tpnxy THixa, a Bi inn Horo sepumut aeaarh Ha GiiuX eroponax. Bualrrn\n\nponvip nparoxyrinia, xii sine HaliGinouy mony.\n\n(Bidn.: possnipu npastonynavaya b/2 i h/2 ).\n\n10, Oninky surpar P na exenayaraniio anromobiaa ayiticmowrs 3a piamasct\nHOKHHINKAMA, (LH 9 1KAX — Le BIEPATH HA OAWH KiNOMeETp MuIXy, Burpara aa\nou HoKaaMKOM cranonaaTh kV? (Vo umysier avrowobins, ky Koedini-\nen ponopaifinocri na oui kiiomerp maaxy), © ANpATH SA /ApyrHae HOKASINKOM\neranonsay kot hap (t z Mae, 20 HHT ABTOMOGID JOsME O”UM KiOMErp,\nuuunxy, ky koeinien aponopuifinocr’ aa oun KixoMerp muuaxy). Ba sKoT uN\nkocri cysapai eirpara aa qua qos HoKAsHKAML (HA Q”UET KiIOMerp miIXy)\n\nGyAyTD Hafivermn, sno ky =\n\n(Bidn.: upu inowsoemi art).\n''6.31\n\nHira rpm dyusniit aa AouOMOroI Mpaniura Touivaas\n\nws\n5) lim () :\n\n1 bynsuil fe) = xsin a aanucarn dbopayay Maxanpena apyroro nopaye\nky it anammxonnst sienos y dopsti Tarpana\n\nsing— 2?\n\ni): ey oe\n\n8. ocaiuiim ynxnit ra no6yaynann ix rpadpixn\n\nztl é x\ney v=T\n\naly inet\n\n9. Y ypuxytimgy jomxnio0 oenonn & qHoMta FocrpHAKT KyTANH NPA OCHOR\ni micoto A saucano opawoxy rink vax, 10 JH Horo Hep porTAMOnasi HA\n\nOchoa tpnxy THixa, a Bi inn Horo sepumut aeaarh Ha GiiuX eroponax. Bualrrn\n\nponvip nparoxyrinia, xii sine HaliGinouy mony.\n\n(Bidn.: possnipu npastonynavaya b/2 i h/2 ).\n\n10, Oninky surpar P na exenayaraniio anromobiaa ayiticmowrs 3a piamasct\nHOKHHINKAMA, (LH 9 1KAX — Le BIEPATH HA OAWH KiNOMeETp MuIXy, Burpara aa\nou HoKaaMKOM cranonaaTh kV? (Vo umysier avrowobins, ky Koedini-\nen ponopaifinocri na oui kiiomerp maaxy), © ANpATH SA /ApyrHae HOKASINKOM\neranonsay kot hap (t z Mae, 20 HHT ABTOMOGID JOsME O”UM KiOMErp,\nuuunxy, ky koeinien aponopuifinocr’ aa oun KixoMerp muuaxy). Ba sKoT uN\nkocri cysapai eirpara aa qua qos HoKAsHKAML (HA Q”UET KiIOMerp miIXy)\n\nGyAyTD Hafivermn, sno ky =\n\n(Bidn.: upu inowsoemi art).\n'

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Math Problem Analysis

Mathematical Concepts

Limits and L'Hôpital's Rule
Taylor and Maclaurin Series
Graphing Functions
Optimization Problems
Cost Analysis

Formulas

L'Hôpital's Rule: lim x→a f(x)/g(x) = lim x→a f'(x)/g'(x)
Maclaurin Series Expansion: f(x) = f(0) + f'(0)x + f''(0)x²/2! + ...
Area of a Rectangle: A = b × h
Cost Function: P = k1V² + k2(1/V)

Theorems

L'Hôpital's Rule
Maclaurin Series Theorem
Optimization Principles

Suitable Grade Level

Undergraduate or Advanced High School Level