8. Which of the following is the Taylor series, centered at a = 1/4, of the function f(z) = tan(I) ? (a) 1 +21 + 21 + , I' t ... ( b ) 1 + 2(x - 7/4) + 4(I - 7/4)2 + - (2 - 71/4)3 +... ( c ) 1 + 5 ( 2 + 7 / 4 ) + 2 ( I + 7 / 4 ) ? + 2 ( I - 7 / 4 ) 3 + ... (d) 1 + 2(1 - 7/4) + 2(I - 1/4)2 + - (2 - 71/4)3 +... (e) 1+1+1 +- 13 +... 9. Find the sum of the following series if it exists: Everge. + 1 n (n + 1 ) 2 01- Lavromni ed) an (a) TH- 1 ( b ) (C) (d) (e) The series is divergent. 10. The solution to the initial value problem y' = I - Iy, y(0) = -1 is given by (a) y = 1-2era/2 (b) y = -1+ ex-/2 (c) y= 1- e-1/2-In2 (d) y =1-2e-12/2 (e) none of these