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This question doubles as 'Is my understanding of what a Taylor polynomial is for, correct?' but In order to write out a Taylor polynomial for a function, which we will use to approximate said funct...
Feb 23, 2018 · When a Taylor series exists, the Taylor polynomial is given simply by truncating the series to finitely many terms. (Taylor polynomials can exist in situations where Taylor series don't)
Sep 12, 2016 · This is reason why those limits in your question are $0$. The idea behind the proof of 'uniqueness of Taylor polynmials' is simple. If $R (x)$ is a polynomial of degree $n$ such that $$R (x) = o ( (x - a)^ {n})$$ as $x \to a$ then $R (x) = 0$ identically. Why?? We use induction on $n$ the degree of polynomial $R (x)$.
Oct 1, 2019 · Why we use an orthogonal polynomial (Hermite, Legendre, or Laguerre, etc.) approximation of any function if Taylor series approximation is already there. And what are the criteria to say that which
I (sort of) understand what Taylor series do, they approximate a function that is infinitely differentiable. Well, first of all, what does infinitely differentiable mean? Does it mean that the fu...
Taylor Series are studied because polynomial functions are easy and if one could find a way to represent complicated functions as series (infinite polynomials) then one can easily study the properties of difficult functions.
This is a McLaurin series, it's a special case of the Taylor series and for some reason the name stuck, McLaurin's series is the name of a Taylor's series about the origin. It came after Taylor's series and McLaurin himself refuted the name, but it stuck. The Taylor's series, as the other answers note is the 'shifted' form of this.
Apr 5, 2020 · Taylor polynomial: the higher the degree, the better the approximation? Ask Question Asked 5 years, 4 months ago Modified 5 years, 3 months ago
Aug 8, 2020 · I have troubles understanding why and when you can substitute your variables in a Taylor series. Could somebody help me explain why that is possible? Especially because the derivative often involve...
Feb 7, 2012 · B For the second matter, the composition, you should consider the properties of the Taylor series. Since there is a broad scope of functions we can compose, you should always pay attention to continuity among other issues. However, in the simplest cases, you can compose a Taylor polynomial with another polynomial, or elementary functions.
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