I would need some help with those questions. Thank you very much!

6x (1 point) Represent the function 3 + x 2 a || || .9 || C3 = C4: Find the radius of convergence R = no as a power series f(x) = 2 cnx\" n: (1 point) Find the convergence set of the given power series: (ac2)" The above series converges for IA R IA (1 point) Find all the values of x such that the given series would converge. (420" Answer: Note: Give your answer in _i_r_1_te_r_\\_r[_r_1_(_)_t'gi_gr_1_ . (1 point) Find all the values of x such that the given series would converge. (ac2)" Answer: Note: Give your answer in interval notation (1 point) Suppose that Find the following coefficients of the power series. Co: Cl: 02: C3: C4: Find the radius of convergence R of the power series. R = (14+x) = 3 1+16:r.2 (1 point) The function f(x) = is represented as a power series: f(x) = 2 six" n=0 Find the first few coefficients in the power series. CO: 01 = 02: 03: C4 = Find the radius of convergence R of the series. R = x (1 point) Let F (x) = / sin(8t2) dt. 0 Find the MacLaurin polynomial of degree 7 for F (x). 0.79 Use this polynomial to estimate the value of / sin(8x2) dx. 0 (1 point) Find Taylor series of function f(x) = ln(x) at a = 5. (f(x) = 2 one: 5)") CO = n 0 cl = 62 = 03 = c4 = Find the interval of convergence. The series is convergent: from x = , left end included (Y,N): to x = , right end included (Y,N): (1 point) Match each of the Maclaurin series with correct function. 1 i (_1)n2x2n+1 ' 2n + 1 0 2x2n+1 A. e27\" B. cos(2x) C. 2 sin(x) D. 2 arctan(x) (1 point) Find the Maclaurin series of the function f(x) = (7x2)e'2x. Determine the following coefficients