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I found that in later activities where we created power series approximations for sets of point charges, students were confused by having to make a choice of $z_o$, the point they are expanding around. In practice, physicists only use Maclaurin series, and if I were to re-do this activity (and the associated maple worksheet), I would switch to using only Maclaurin series, and studying something like a Lorentzian or perhaps a Gaussian (since I think the Lorentzian shows up in homework) instead of looking at $\sin(x-\pi/6)$. An interesting option (if it weren't done in the homework) would be to look at a lorentzian when expanded in either x or 1/x, to see how one captures the small-x behavior and the other captures the large-x behavior.

To be more specific, when asked to create an approximation for V at large $x$ for a set of point charges, students tried selecting a large $x_o$, which I think was motivated by the idea promulgated in this activity and its associated maple worksheet that to get a better approximation you need to expand around the point that you're interested in.

David


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