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MF71: Tangent lines and conics of polynumbers

This video introduces tangent lines and tangents conics of polynomials, using the very simple high school approach through polynumbers and bipolynumbers. We first define constant, linear, quadratic, cubic, quartic and quintic polynumbers in terms of the degree. Then we make some subtle shifts in the Taylor bipolynumber to find the Taylor expansion of a polynomial at a point c, and then using that to define the 1st tangent, 2nd tangent and so on. We will see how these are useful in computing approximations to the values of a polynomial.This lecture is part of the MathFoundations series, which tries to lay out proper foundations for mathematics, and will not shy away from discussing the serious logical difficulties entwined in modern pure mathematics. The full playlist is at http://www.youtube.com/playlist?list=PL5A714C94D40392AB&feature=view_all
Length: 36:29

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