h(x) = x ln(1 + 2x)

Expand the function in a power series Σ anx" with center c = 0. Find anx". n=0 1 4+5x (Express numbers in exact form. Use symbolic notation and fractions where needed. For alternating series, include a factor of the form (-1)" in your answer.) anxn = Determine the interval of convergence. (Give your answers as intervals in the form (*, *). Use symbol ∞ for infinity, U for combining intervals, and appropriate type of parenthesis" (", ") ", [" or "]" depending on whether the interval is open or closed. Enter DNE if interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) XE

Suppose a power series converges if | 4x - 8 | ≤ 40 anddiverges if | 4x - 8 | > 40. Determine the radius and interval of convergence.

Find all the values of x such that the given series would converge. (– 1)"8".x" n=1 (Vn + 10) The series is convergent from x = left end included (enter Y or N): to x = ,right end included (enter Y or N):