Aplicação do polinômio de Taylor na aproximação da função Seno
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Data
2014-07-03
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Universidade Federal de Goiás
Resumo
In this work the main goal is focused on applying the theory of Taylor polynomial
approximations applied on the trigonometric function defined by f : [0;
2 ] ! R, where
f(x) = sin(x). To achieve this goal, eight sections were developed, in which initially a
reflection on the problem and the need to obtain the values in this respect in that it is
wide angle measure x is presented. Is presented and subsequently treated a problem
involving the movement of a pendulum, which uses the approximation sin(x) x
where x belongs to a certain range. In the sections that follow a literature review of
the theories of differential and integral calculus is presented, and the related theory
of Taylor approximation of functions by polynomials. Later we used these theories
to analyze and determine polynomials approximating the function f(x) = sin(x) in
a neighborhood of the point x = 0, and estimate the error when we applied these
approaches. At this time the error occurred due to the approach used in the pendulum
problem was also analyzed. Finally a hint of practice to be held in the classroom using
the theories treated here as well as the study of the problem of heat transfer in a bar
through the theory of Fourier activity is presented.
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Citação
CURI NETO, Emilio. Aplicação do polinômio de Taylor na aproximação da função Seno. 2014. 75 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2014.