Aplicação do polinômio de Taylor na aproximação da função Seno
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...
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| Tipo de documento: | dissertação |
| Estado: | Versão publicada |
| Data de publicação: | 2014 |
| País: | Brasil |
| Recursos: | Universidade Federal de Goiás (UFG) |
| Repositório: | Repositório Institucional da UFG |
| Idioma: | português |
| OAI Identifier: | oai:repositorio.bc.ufg.br:tede/3493 |
| Acesso em linha: | http://repositorio.bc.ufg.br/tede/handle/tede/3493 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Aproximações polinomiais Funções trigonométricas Polinômio de Taylor Polynomial approximations Trigonometric functions Taylor polynomial MATEMATICA::MATEMATICA APLICADA |
| 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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