Hello everyone, in this opportunity, I want to talk about the Taylor series
Many of us have come across limit, derivative, and/or integral calculus of complicated functions. Taylor's theorem is named after the British mathematician Brook Taylor. This theorem allows us to approximate any function through a polynomial, so the above calculations are simpler in this type of function.
(Taylor Series) Let f be a real or complex function infinitely differentiable at the point x = a then the Taylor series of f (x) centered on a is:
Note that T (x) is the only polynomial that satisfies:
- Example: The Taylor polynomial of order six, eight and ten for f (x) = sin (x) / x centered at x = 0 is:*
Notes that the higher the order of the polynomial the better the approximation
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