Taylor's theorem

in science •  8 years ago 

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:

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Note that T (x) is the only polynomial that satisfies:

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  • Example: The Taylor polynomial of order six, eight and ten for f (x) = sin (x) / x centered at x = 0 is:*

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Notes that the higher the order of the polynomial the better the approximation

enjoy and upvote, follow me @falcao12

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Nice job. Are you able to embed the latex in there or are those images?

Thanks, they are images, it would be wonderful to be able to write in latex here