Question

Determine the Taylor series about the poin x0 for the given function. Also determine the radius of convergence of the series.

Answer 1

sin x, x0=0

Answer 2

determine or remember?
power series for sine is well known
do you have to do it by hand?

Answer 3

successive derivatives are
\[\cos(x)\\
-\sin(x)\\
-\cos(x)\\
\sin(x)\] and then they repeat

Answer 4

put \(x=0\) and you get
\[0,1,0,-1,0,1,0,-1,...\]

Answer 5

making the power series
\[x-\frac{x^3}{3!}+\frac{x^5}{5!}-...\]

Answer 6

Thanks