Published in Scientific Papers. Series "Journal of Young Scientist", Vol. 8
Written by Marius CEAUȘ
It is common belief that the first person in history who ever used infinite series approximations to trigonometric functions was the Indian mathematician Madhava (1340–1425 bC), the founder of the Kerala astronomy school, who deduced some approximation formulas for trigonometric functions by geometric arguments. In the West, the intuitive idea of more general Taylor series was given by the Scottish mathematician James Gregory, but they were formally introduced by the English mathematician Brook Taylor in 1715. Taylor series centered at 0 are also called Maclaurin series, in the honour of the Scottish mathematician Colin Maclaurin, who extensively used this special case in his works in the 18th century. The partial sums of a Taylor series are called Taylor polynomials. The Taylor series are very powerful methods used to function approximations (numerical approximations, integrals, differential equations, asymptotic calculus). In this article we use the asympthotic expressions of Taylor series in order to calculate function limits.
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