Donnie Smith Assignment Section 8.6 due 04/28/2017 at 11:59pm MST Sharma MAT 266 ONLINE B Spring 2017 c3 = 1. (1 point) Consider the function c4 = 1 1 x3 Find the radius of convergence R of the series. R= . Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if n 2n 2 2 4 the series were n=0 3 x , you would write 1 + 3x + 3 x + 3 6 4 8 3 x + 3 x . Also indicate the radius of convergence. Partial Sum: Radius of Convergence: Answer(s) submitted: Answer(s) submitted: 1+x3+x6+x9+x12 1 (incorrect) 6x = cn xn . (7 + x) n=0 Find the first few coefficients. c0 = (correct) 4. (1 point) Suppose that 2. (1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f (x) = Answer: f (x) = + + x3 1 + 4x + c1 = + c2 = + c3 = What is the interval of convergence? Answer (in interval notation): c4 = Find the radius of convergence R of the power series. R= . Answer(s) submitted: Answer(s) submitted: (incorrect) 3. (1 point) The function f (x) = power series f (x) = 8 1+4x2 is represented as a (incorrect) n cn x . 5. (1 point) The function f (x) = power series n=0 Find the first few coefficients in the power series. 6 (12x)2 is represented as a f (x) = c0 = cn x n . n=0 Find the first few coefficients in the power series. c0 = c1 = c2 = c1 = 1 c2 = Partial Sum: Radius of Convergence: c3 = Answer(s) submitted: c4 = Find the radius of convergence R of the series. . R= (incorrect) 8. (1 point) The function f (x) = 8x ln(1 + 2x) is represented as a power series Answer(s) submitted: f (x) = cn x n . n=0 Find the FOLLOWING coefficients in the power series. c0 = c1 = c2 = c3 = c4 = (incorrect) 6. (1 point) The function f (x) = power series 3x2 (14x)2 is represented as a f (x) = cn xn . Find the radius of convergence R of the series. R= . n=0 Find the first few coefficients in the power series. Answer(s) submitted: c1 = c2 = c3 = c4 = (incorrect) c5 = 9. (1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. Find the radius of convergence R of the series. R= . f (x) = ln(6 x) Answer(s) submitted: Answer: f (x) = + + + What is the radius of convergence? Answer: R = (incorrect) Answer(s) submitted: 7. (1 point) Consider the function ln(1 + 15x). Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. n 2n For example, if the series were n=0 3 x , you would write 2 2 4 3 6 4 8 1 + 3x + 3 x + 3 x + 3 x . Also indicate the radius of convergence. (incorrect) 2 + + n 2n For example, if the series were n=0 3 x , you would write 2 2 4 3 6 1 + 3x + 3 x + 3 x . Also indicate the radius of convergence. 10. (1 point) Consider the function arctan(x/6). Partial Sum: Radius of Convergence: b) Use part a) Rto write the partial sum for the power series which represents arctan(x2 )dx. Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if n 2n 2 2 4 the series were n=0 3 x , you would write 1 + 3x + 3 x + 3 6 4 8 3 x + 3 x . Also indicate the radius of convergence. Partial Sum: Radius of Convergence: Write the first 4 nonzero terms. Also indicate the radius of convergence. Answer(s) submitted: Partial Sum: Radius of Convergence: R c) Use part b) to approximate the integral 00.5 arctan(x2 )dx. (incorrect) Answer(s) submitted: 11. (1 point) a) Consider the function arctan(x2 ). Write a partial sum for the power series which represents this function consisting of the first 4 nonzero terms. (incorrect) c Generated by WeBWorK, http://webwork.maa.org, Mathematical Association of America 3