The discussion focuses on deriving the Taylor series for the function ln[(x - h²) / (x + h²)] using Taylor's Theorem. Participants emphasize the necessity of knowing the center of expansion, denoted as 'a', to properly formulate the series. The standard Taylor series formula is referenced, highlighting the relationship between the function's derivatives and the expansion terms. The conversation concludes with a suggestion to clarify the problem statement with the professor for further guidance.
PREREQUISITESStudents studying calculus, mathematicians interested in series expansions, and educators seeking to clarify Taylor's Theorem applications.
Isn't there any more to this question? Usually, if they want a Taylor's series, they'll give information like "expanded around a = 1" or the like. This would mean that the Taylor's series would look like ##a_0 + a_1(x - 1) + a_2(x - 1)^2 + \dots + a_n(x - 1)^n + \dots##.Alec11 said:Homework Statement
Find the Taylor series for:
ln[(x - h2) / (x + h2)]
Alec11 said:Homework Equations
f(x+h) =∑nk=0 f(k)(x) * hk / k! + En + 1
where En + 1 = f(n + 1)(ξ) * hn + 1 / (n + 1)!
The Attempt at a Solution
ln[(x - h2) / (x + h2)] = ln(x-h2) - ln(x + h2)
This is as far as I have been able to get. I don't understand what to set x and h to, and without that I don't think I can do much else.[/B]
No, I gave you all of the information that is given. I assume they just want me to write out the first few terms of the series without evaluating it.Mark44 said:Isn't there any more to this question? Usually, if they want a Taylor's series, they'll give information like "expanded around a = 1" or the like. This would mean that the Taylor's series would look like ##a_0 + a_1(x - 1) + a_2(x - 1)^2 + \dots + a_n(x - 1)^n + \dots##.
If a = 0, the series is a Maclaurin series.
My point is that you can't write the first few terms without knowing what the "center" of the expansion is. IOW, without knowing what a is in all of the x - a terms. My advice is to contact your professor and ask him/her to clarify this question.Alec11 said:No, I gave you all of the information that is given. I assume they just want me to write out the first few terms of the series without evaluating it.
It is possible if you're using Taylor's Theorem in terms of h that I specified in the OP.Mark44 said:My point is that you can't write the first few terms without knowing what the "center" of the expansion is. IOW, without knowing what a is in all of the x - a terms. My advice is to contact your professor and ask him/her to clarify this question.
This is a different form than I have seen Taylor's Theorem. The usual way the Taylor Formula is presented isAlec11 said:It is possible if you're using Taylor's Theorem in terms of h that I specified in the OP.