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Math Help - [SOLVED] Little doubt : Taylor's polynomial

  1. #1
    MHF Contributor arbolis's Avatar
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    [SOLVED] Little doubt : Taylor's polynomial

    I must find P_{5,0}(x), in other words the Taylor's polynomial of order 5 evaluated in 0 of the function f(x)=\frac{\sin (x)}{1+x^2}. But it says to consider the Taylor's polynomials of the functions \sin (x) and \frac{1}{1+x^2}. I found them, so my bet would be to multiply them... but as you can imagine, I got a polynomial of degree 10. So my little doubt is : I only take on consideration the terms of degree \leq 5 and I'm done? In other words, I throw up the terms of greater degree than 5 and I get the Taylor's polynomial of f of order 5. Am I right?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by arbolis View Post
    I must find P_{5,0}(x), in other words the Taylor's polynomial of order 5 evaluated in 0 of the function f(x)=\frac{\sin (x)}{1+x^2}. But it says to consider the Taylor's polynomials of the functions \sin (x) and \frac{1}{1+x^2}. I found them, so my bet would be to multiply them... but as you can imagine, I got a polynomial of degree 10. So my little doubt is : I only take on consideration the terms of degree \leq 5 and I'm done? In other words, I throw up the terms of greater degree than 5 and I get the Taylor's polynomial of f of order 5. Am I right?
    That is based upon the conventions that your book uses. I have seen "order" used to denote number of terms and degree of a polynomial. But offhand, I would say that is the correct assumption.
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