Find a power series representation for the function O 1 . f (y ) = (-1)n 2n+lyn 1 n=0 f(y ) = 2ty O 2. f(y) = 1 2n+1 ?" n=0 O 00 3. f(y) = (-1)"2y" n=0 4. f(y) = E (-1)ngn+1 yn n=0 O 5. f(y) = 2ntlyn n=0\fDetermine an expression for b6 if f(6) (6) 1. b6 = 5! f(x) = > bn(x - 5)" . f (6) (5) n=0 2. b6 = 6 f (6) (5) 3. b6 = 6! f (5) (6) 4. b6 = 5! f (5) (5) 5. b6 = 6!Find the Taylor series centered at a = 0 for (-1)n22n M . 2n f(x) = cos(2.) . n=0 (2n)! 2 . iM 8 (-1)n22n (2n)! M 8 (-1)n22n 3. .2n n=0 n! 100 4. (2n)! n =1 00 2n 5 . n (2n)! n =1 M : (-1)n22n 6. n! n=0Find a power series representation for the function 1. f(x) = (In(2) )" n! f(x) = 27 n=0 on (-0o, 00). 2. f(x) = (In(2) )" n+1 n! n=0 3. f(x) = (In(2) )" 2n n! n=0 00 4. f(x) = (In(2) )" an 2n! n=0 00 5. f(x) = (In(2) )" n! n=2