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If you approximate a complicated function with a Taylor Series to the first order, what will this approximation look like on a graph? And what are the orders? I just started studying Taylor approximation in Physics and I am hearing "first order, second...etc". I don't know what they refer to, it might be a linguistic problem for me because I studied in Arabic before that.

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    $\begingroup$ The oder refers to the degree of the polynomial you obtain by truncating your infinite Taylor series. $\endgroup$
    – Gary
    Commented Jan 31, 2022 at 5:42
  • $\begingroup$ I wrote a couple of blog posts about this which include illustrations: here. Also I cannot recommend too much that you visit desmos.com and have it make some graphs for you so that you can see what it looks like. $\endgroup$
    – MJD
    Commented Jan 31, 2022 at 16:23

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The first order Taylor approximation will be linear, second order will be quadratic, etc.

So you can think of the first order approximation as the tangent line to the true function at the point you are choosing to expand from.

Think "order" as "degree" for Taylor's theorem.

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