Taylor and Maclaurin series questions
1. Find the Taylor series for f(x) = cos (3x) centered at a = (Pi/2). Find its radius of convergence.
2. Let f(x) = (1+x)^(-1/2)
a) Find the Maclaurin series for f.
b) Use the series found in 2a to find the maclaurin series for (1+x^2)^(-1/2) and use that result to find a Maclaurin series for sinh^-1 (x).
I cannot figure out how to do these. For 1, I substituted the 3x for x in the cos(x) series... what do I do from there? I know I have to put (x-a) at the end for the center.
For 2, I have no idea what to do. It says to use the binomial series, which we didn't really cover. It's a bonus on a homework.