A new representation of Lagrange’s theorem in differential calculus
It is found a new representation of the mean value Lagrange’s theorem in the differential calculus. Any function increment can be expressed through the derivatives in the ending points of a given closed interval. Mean values of the Lagrange derivative and our theory derivative are coincided, but t...
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| Date: | 2014 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут проблем штучного інтелекту МОН України та НАН України
2014
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| Series: | Искусственный интеллект |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/85304 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A new representation of Lagrange’s theorem in differential calculus / L.P. Mironenko, I.V. Petrenko // Искусственный интеллект. — 2014. — № 2. — С. 129–133. — Бібліогр.: 5 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | It is found a new representation of the mean value Lagrange’s theorem in the differential calculus. Any
function increment can be expressed through the derivatives in the ending points of a given closed interval.
Mean values of the Lagrange derivative and our theory derivative are coincided, but the middle points are
different. Our theory allows easily find the middle point and it is not so easy according to Lagrange’s
theorem. Furthermore, our theory makes it possible to formulate the second mean value theorem in integral
calculus, as it is a consequence of differential theorem. |
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