91Ó°ÊÓ

Find the Taylor polynomial of the indicated degree \(n\) at the indicated point \(c\) for the following functions: (a) \(f(x)=e^{x}, n=6, c=0\) (b) \(f(x)=\sin x, n=4\) and \(6, c=0\) (c) \(f(x)=\sin x, n=5, c=2\) (d) \(f(x)=\tan x, n=6, c=0\) (e) \(f(x)=\ln x, n=4, c=1\)

Create a 17-frame movie, whose frames show filled red circles of radius \(1 / 2\) centered at the points \((4 \cos (j \pi / 8), 4 \sin (j \pi / 8)), j=0,1, \ldots, 16\). Make sure that all the circles are drawn on the same set of axes, and that they look like circles, not ellipses.