1. What is the interval of convergence for series _ LD=In(x - 3)n a. (2, 4) b. (0,4) C. (-3,3) d. (-4,4) 2. Use a power series to represent the following function: f (x) Joo x2+2 a. Ln=0 an+1 for x 2 d. Too xn+ 2 2n=0 27+1 for x > 212 3. Find the Taylor series for at x = 1. a. Too (-1)n Ln=0 an (x - 1)n b. Too (-1)n Zn=0 an+1 (x - 1)n -1 C. 2n=0 an+1 (x - 1)n d. Ln=0 in (x - 1)n 4. The error function of f(x) = Left dtis used in the field of probability. Find the approximate value of er f(1.5) using the first four terms of the Maclaurin series for e-t2 a. 0.4231 b. 0.8210 C. -0.2116 d. -0.1410 5. Identify the characteristic equation of the following differential equation and the roots of the characteristic equation. a. CE: 412-471 + 1 = 0; repeated real root: b. CE: 412-421 + 1 = 0; repeated real root: 1 1 2' 2 c. CE: 412-41 + 1 = 0; repeated real root:- d. CE: 412-41 + 1 = 0; repeated real root: - _ _ 2'2