10. Find the radius and interval of convergence of the power series (-3)"X" Vn+
(a) Find the series' radius and interval of convergence. Find the values of x for which the series converges (b) absolutely and (c) conditionally x" Σ n=0 vn +3
12. (10 points) Find the radius and interval of convergence of the following power series. Be sure to check the endpoints if the interval is finite! M8 (x – 5)" (-3)n+1m2 n=3
Find the interval of convergence and radius of convergence for the power series Š(+1)* x* (2k) b=0
Find the radius of convergence, R, of the series. 0 (-1)"x" Σ Vn n = 1 R = 1 Find the interval, I, of convergence of the series. (Enter your answer using interval nota I = (-1,1) X
3. Find the radius and interval of convergence for the following power series. (x-4)" 9 n=0
0o 5. (a) (10) Let f(x), and assume that the radius of convergence of the power series is 3. Find the radius of convergence R2 for f"() Also find the appropriate power series for f"(2). (b) (10) Let z 16i. Find a formula for each of the two square roots z0, 31 of z. Graph both square roots in the complex plane, and identify each. 0o 5. (a) (10) Let f(x), and assume that the radius of convergence of the...
Q1. (10 pts) (a)Find the center, radius, and interval of convergence of the power series En=o 4n(x + 2)" !!!Do not forget to check the end points of the interval for convergence. (b) Write the first 5 terms of this series. So define the 4th degree polynomial approximation, P4(x) for the given series with the first 5 terms. Can we use P4(x) to approximate the series at x = -2.1? Explain.
Find the interval and radius of convergence of the power series (x + 1)k 3k 22 k-1
Find the radius of convergence and the interval of convergence of the following power series. Make sure to clearly indicate and justify whether or not the end points of the interval are included in the interval of convergence. Σ (3.0 - 6)" 2n n +1 n=1
Find the radius and interval of convergence of the following power series function, including the analysis of any endpoints of the interval. (x - 3)" f(x) = 2 31 n=1