1. The Taylor series expansion for f(x) centered at c is a0+a1($C)+a2($C)2 +a3(a:c)3+~~+ak(xc)k+~~ = Zonesc)\" n=1 ('0 where an 2 f (c) . n! 71' In this problem, you will nd the Taylor series expansion for f (51:) = cosa: centered at 2 we mare) as), Ms)- 71' (b) Write the Taylor series expansion for f (x) centered at 5. Express your answer in both E and ~ ~ ~ notation (with at least three terms written out). 2. Write the geometric series with the rst term a1 = 3 and the common ratio 7' = 2. Express your answer in both 2 and ~ ~ ~ notation (with at least three terms written out)