Find the radius of convergence of the following power series. IM8 (3x - 10) n 15
15. Use integrability of power series to find the sum n=1 in the form of an elementary function within the radius of convergence of S(a)
15. Use integrability of power series to find the sum n=1 in the form of an elementary function within the radius of convergence of S(a)
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 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 of convergence and interval of convergence of the series. Please indicate and explain the tests you are using for the endpoints. (12pts.) iM8 (2x – 1)" I.C. 5" In n=1 R.C.
Problem 7. (10 points) Find the center, radius of convergence and interval of convergence for the power series IM8 (-1)'(x - 1)" m2 +1 Center: x = Radius of Convergence: Interval of Convergence (use interval notation): Note: You can earn partial credit on this problem. Problem 8. (10 points) Find the Taylor polynomial of degree 2 for $(x) = + x centered at a -6. 73(x) =
f(x) = (3x)/(1+x) Find a Power Series for f(x), including the radius and interval of convergence, in two separate ways: 1. Constructing it from the sum of a Geometric Series 2. Manipulating a known series
Find the radius of convergence of the following power series: ю 3 zn 5(n/2) n=1
2. Find the radius of convergence of the power series 5(n/2) n=1
Problem 5 Find the radius and interval of convergence for the following Power Series: oo (-1)n n-l nn n2n n-l n+1
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...