6. Find the series' interval of convergence and, within this interval, the sum of the series as a function of x. [ 30 x n= 0 Find the series' interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The interval of convergence is (Type a compound inequality. Use integers or fractions for any numbers in the expression.) O B. The series converges only at x = .(Type an integer or a fraction.) O C. The series converges for all values of x. The sum of the series is _ 3"x" = n=0 7. Find the series' interval of convergence and, within this interval, the sum of the series as a function of x. n=0 Find the series' interval of convergence. Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The interval of convergence is Simplify your answer. Type a compound inequality. Use integers or fractions for any numbers in the expression.) O B. The series converges only at x = Simplify your answer. Type an integer or a fraction.) O C. The series converges for all values of x. The sum of the series as a function of x is g(x) = 8. Use a geometric series to represent each of the following functions as a power series about x = 0. Find the interval of convergence a. f(x ) = 6-x b. g(x) =- x - 4 a. The power series representation for f(x) is _ ( n=0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.) b. The power series representation for g(x) is > xn n=0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.)9. For what values of it does the series below converge? What is its sum? What series do you get if you differentiate the given series term by term? For what values of it does the new series converge? What is its sum? 1...l 5+; 52+ 4- *1" *5\"+ 4t! )16\" l 4 (I l For what values of x rices the series converge? Select the correct choice below and. if necessary. ll in the answer box to complete your choice. D A- The series converges for {Type a compound inequality. Simplify your answer. Use integers or fractions for any numbers in the expression.) 0 B- The series converges only at x = . [Type an integer or a simplied fraction} 0 C. The series converges for all values of x. The sum of the series within its interval: of convergence is What series do you get il'you differentiate the given series term by term? For what values of it does the nevir series converge? Select the correct choice below and. if necessary. tilt in the answer box to complete your choice. 0 E- The series converges for {Type a compound inequality Simplify your answer. Use integers or fractions for any numbers in the expression.) 0 B. The series converges only at x = . [Type an integer or a simplied fraction.) 0 c. The series converges for all values of x. The sum of the new series within its interval of convergence is