MAT 302 Assignment Problem 9.8

MAT 302 Assignment Problem 9.8 | Borough of Manhattan Community College

9.8 Power Series

Question 1

Consider the power series

Find the radius of convergence R.R. If it is infinite, type "infinity" or "inf".

Question 2

Consider the power series

Find the radius of convergence R.R. If it is infinite, type "infinity" or "inf".

Question 3

Consider the power series

Find the radius of convergence R.R. If it is infinite, type "infinity" or "inf".

Question 4

Consider the power series

Find the radius of convergence R.R. If it is infinite, type "infinity" or "inf".

Question 5

Consider the power series

Find the radius of convergence R.R. If it is infinite, type "infinity" or "inf".

Question 6

(1 point) If ∑Cn(x−4)n∑Cn(x−4)n converges at x=9x=9 and diverges at x=12x=12, what can you say about:

Question 7

 Consider the series

Find the interval of convergence of this power series by first using the ratio test to find its radius of convergence and then testing the series' behavior at the endpoints of the interval specified by the radius of convergence.
interval of convergence =

(Enter your answer as an interval: thus, if the interval of convergence were −3<x≤5−3<x≤5, you would enter (-3,5]. Use Inf for any endpoint at infinity.)

Question 8

 Consider the series

Find the interval of convergence of this power series by first using the ratio test to find its radius of convergence and then testing the series' behavior at the endpoints of the interval specified by the radius of convergence.
interval of convergence 

(Enter your answer as an interval: thus, if the interval of convergence were −3<x≤5−3<x≤5, you would enter (-3,5]. Use Inf for any endpoint at infinity.)

Question 9

(1 point) Match each of the power series with its interval of convergence..

Question 10

(1 point) Find all the values of x such that the given series would converge.

Question 11

(1 point) Find all the values of x such that the given series would converge.

Question 12

(1 point) Find all the values of xx such that the given series would converge.