The Taylor series #math

The Taylor series is a mathematical representation that allows a function to be rewritten as an infinite sum of terms. These terms are calculated from the derivatives of the original function, evaluated at a specific point (in this case, centered at the origin x = 0, which is formally known as the Maclaurin series). The main purpose of this tool is to approximate complex or non-polynomial functions, such as sine, cosine, or exponential functions, using polynomials. This is fundamental in numerical analysis and computing, since a processor cannot directly calculate a sine function, but it can perform the additions and multiplications required by a polynomial. The animation shows the approximation of the function f(x) = sin(x). The variable n dictates the number of algebraic terms that make up the summation. Physically, the graph shows how each time we increase the number of terms {x, -(x^3)/(3!), etc.}, the higher-degree polynomial "bends" to more accurately hug and replicate the behavior of the original wave. The larger the summation, the smaller the margin of error in the approximation. #geometry #physics

Видео The Taylor series #math канала homopensando