Expand the function , in a power series E a,x" with center e = 0. Find a,x". 7+8x n=0 (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.) a„x" = 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.)

dx S 16+4x2

For each of the following, factor the matrix A into a product QDQ" where Q is orthogonal and D is diagonal. -7 1 1 (a) A = -1 -7 1 -7 -1 D = -4 -2 2 (b) A = -2 -3 2 3 -3 D = || ||