I'm completely lost on what to do here.

(a) Find the $3$rd degree Taylor polynomial for $f(x) = \tan(2x)$, around $x = 0$.

(b) Suppose you know $f^{(4)}(x) < 130$ if $0 < x < .1$; use this and (a) to approximate $\tan(.2)$, and determine the maximum error possible in doing so.

I understand that the second part of the problem indicates using the Lagrange remainder but I am not sure how to go about approximating the value other than plugging $(.2)$ into the Taylor polynomial. Any help would be greatly appreciated!


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