Taylor and Maclaurin Series - help please?

Question

(a) Find the maclaurin series for f(x)=sin2x and the radius of convergence

(b) Find the Taylor series for f(x)=lnx centered at a=2

You don't have to show all the work but try to explain please!

Answer 1

sin(2x) = 2x-(2x)^3/3! +(2x)^5/5!+(-1)^n-1*
(2x)^2n-1/(2n-1)!++
r = infinity
lnx = ln2 + (x-2) *1/2 -(x-2)^2 (1/4)/2!+++
r= Ix-2I<1 x-2 <1 x<3
and 2-x<1 x>1