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This chapter presents basic ideas of Descartes’ Analytic Geometry playing a crucial role in Calculus. Applications to problems in economics are given. We study Descartes method of tangents to algebraic curves, especially for polynomial curves. Horner’s Rule for polynomials is given. Descartes’ Rule of Signs is proved. Descartes’ Method is applied to determine tangents to inverse and implicit functions.

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Descartes’ Analytic Geometry

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  • 发表日期：

    2025年

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  • Sergey Khrushchev

摘要

This chapter presents basic ideas of Descartes’ Analytic Geometry playing a crucial role in Calculus. Applications to problems in economics are given. We study Descartes method of tangents to algebraic curves, especially for polynomial curves. Horner’s Rule for polynomials is given. Descartes’ Rule of Signs is proved. Descartes’ Method is applied to determine tangents to inverse and implicit functions.