{"id":14,"date":"2024-07-24T21:02:10","date_gmt":"2024-07-24T21:02:10","guid":{"rendered":"https:\/\/authorwebservices-xl.net\/ArchwayPublishing\/856702\/?page_id=14"},"modified":"2026-04-24T12:29:08","modified_gmt":"2026-04-24T12:29:08","slug":"home","status":"publish","type":"page","link":"https:\/\/authorwebservices-gem2.net\/AuthorHouseUK\/874420\/","title":{"rendered":"HOME"},"content":{"rendered":"\n

Calculus Without Limits:<\/strong><\/strong><\/strong><\/strong><\/h1>\n\n\n\n

An Algebraic\u2013Geometric Construction of the Derivative<\/strong><\/strong><\/strong><\/strong><\/strong><\/strong>
By: Davit Kapanadze<\/strong><\/strong><\/strong><\/p>\n\n\n\n

This paper presents an algebraic and geometric\u2013functional approach to introducing the derivative for elementary functions without using limits. The derivative is defined as a functional correspondence between the abscissa of a point on the graph of a function and the slope of the unique tangent line drawn at that point (the X\u2013K correspondence).

The method is developed systematically starting from single-variable polynomial functions by introducing the notions of multiple roots and tangency through an algebraic condition of repeated intersection. On this foundation, the derivative function is constructed and key differentiation rules are established, including the sum, product, quotient, and composite function rules.

The approach is then extended to rational power functions, exponential functions, logarithmic functions with an arbitrary base, and trigonometric functions, yielding the same derivative formulas as in classical analysis.

Finally, the increment of a function and the differential are interpreted geometrically via the tangent line, and the classical limit definition of the derivative arises as an analytical formalization of this geometric differential. The results demonstrate both mathematical consistency and strong pedagogical potential for secondary and undergraduate instruction.<\/h4>\n\n\n\n
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About The Author<\/strong><\/strong><\/h5>\n\n\n\n

Davit Kapanadze is a Doctor of Pedagogical Sciences and a researcher in mathematics education from Georgia.\n\nHis scientific work focuses on the conceptual foundations and teaching of differential calc\u2026<\/p>\n\n\n\n

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\"Book<\/figure>
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Buy The Book<\/strong><\/h5>\n\n\n\n

Discover derivatives without limits through a clear algebraic and geometric approach, making calculus intuitive while mastering differentiation rules for elementary functions with confidence.

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ISBN 13 (SOFT): 9798823096607

ISBN 13 (eBook): 9798823096614
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Calculus Without Limits: An Algebraic\u2013Geometric Construction of the DerivativeBy: Davit Kapanadze This paper presents an algebraic and geometric\u2013functional approach to introducing the derivative for elementary functions without using limits. The derivative is defined as a functional correspondence between the abscissa of a point on the graph of a function and the slope of the unique tangent line drawn at that point (the…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-home.php","meta":{"footnotes":"","_members_access_role":[],"_members_access_error":""},"class_list":["post-14","page","type-page","status-publish","hentry"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t