1.)

Given the power series (-2)" (@ + 6) ". n= Vn Find the radius of convergence, R. and the interval of convergence, I . R = 1/2 I = (-3/2,-1/2]Given the power series (x - 6)" n=1 n(-6)n Find the radius of convergence, R. and the interval of convergence, I R I =Given the power series DO 7" (x - 6) n +6 n=1 Find the radius of convergence, R. and the interval of convergence, I . R IGiven the power series DO (-1)"(6: + 5)" n=1 7" (n2 + 10) Find the radius of convergence, R. and the interval of convergence, I . R = -7/6 I = [11/6,50/6]This is a multipart problem. Submit your answer for the first part before proceeding to the second. Given the function 3x2 f(I) = 1+ x6 Part 1: A Find the power series representation of f centered at 0. f(x) = Find the radius of convergence, R. and the interval of convergence, I of this series. R = = Part 2:This is a multipart problem. Submit your answer for the first part before proceeding to the second. Given the function f(I) = 4-1 Part 1: A Find the power series representation of f centered at 0. f(I) = 7=1 Find the radius of convergence, R. and the interval of convergence, I of this series. R = Part 2:This is a multipart problem. Submit your answer for the first part before proceeding to the second. Given the function f(I) = - 4 Part 1: A Find the power series representation of f centered at 0. f(x) = > Find the radius of convergence, R. and the interval of convergence, I of this series. R = Part 2:This is a multipart problem. Submit your answer for the first part before proceeding to the second. Given the function f(I) = p' - 1 Part 1: A Find the power series representation of f centered at 0. f(*) = > (x)~(2)*(-1)~(n)*(x)(6n) n=0 Find the radius of convergence, R. and the interval of convergence, I of this series. R 1 = (-1,1) Part 2:This is a multipart problem. Submit your answer for the first part before proceeding to the second. Given the function f(I) = 64 + 13 Part 1: A Find the power series representation of f centered at 0. 00 f(I) = n= Find the radius of convergence, R. and the interval of convergence, I of this series. R = I Part 2:Use power series to approximate the definite integral with |error)