The problem involves finding the coefficient a3 in the Taylor series expansion of the function f(x) = x³ln(1+x²) about x = 0. Participants are exploring the nature of Taylor series and the specific coefficients associated with this function.
The discussion is ongoing, with participants questioning the evaluation of derivatives at zero and clarifying terminology related to derivatives. Some have identified that f(0) = 0 and f'(0) = 0, while others are prompted to consider the second and third derivatives.
There is uncertainty regarding the behavior of the function and its derivatives at x = 0, which may affect the determination of the Taylor series coefficients. Participants are navigating the implications of these evaluations in the context of the problem.
How do you normally go about finding the coefficients of the terms in a Taylor's series? In this case, it's a Maclaurin series.lmannoia said:Homework Statement
Let f(x) = x3ln(1+x2), and let the summation (from n=0 to infinity) anxn be the Taylor series for f about 0. Then what is a3?
Homework Equations
The Attempt at a Solution
What?! I definitely don't expect the answer, but does anyone know how I could go about finding this out from the vague information given about the summation?