Question

Find the Maclaurin series for f(x) = -3cos(2x). Show your work using the formula for finding a Macluarin series. Write out at least 4 non-zero terms of the series.

Answer 1

Solutions Given f(x) = - 3 CO3(22) we know that Mallaurin series formula is given by fraude flo) + x firm the " OD + hoe f "0) + -- 4 =-3 Here f(x) = - 3 cos (22) Flo)= =3 casco) = -3/1 = -3. 7 F10) = - 3 f'(%) = o bainc 2x) = f'(o) = 0 f(x) = 12 Cos (2A) = f'O) = 12 f(3) = -248in (2x) = fillo) = -246n (o) = 0 -) fo) = 0) 7494 = - 48 Cos(224z file = -48 6Q02–48 = f 0) = - 48

s from gb fincau) => fyo) = 96 sinco) . - fro) = 0 - and gained = 192 C08C2%) =) fľO) = 192.0080 lo) = 192] plug the value of fros, fo, flo), fo.. - in equation ③ we get frez -3 +240 + 2 x 12 +7° xo - mt xuß - + 4,10 + x (192) + -- .. Afm) = -3 + matt - 48 mt + 193 306 --- {P= 33+ 6x5 mx+ *6+ . ! 41. 6! . this is our required Mactaurines series