Find the first four nonzero terms of the taylor series about 0 for the function f(x)=x4sin(6x). note that you may want to find these in a manner other than by direct differentiation of the function.

The quickest way to get the series is if you already know the series for sine:

Then just multiply the series by to get

The first four nonzero terms are simply the first four terms:

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

i believe the answer is the polygon, heptagon.