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.Donnie Smith Sharma MAT 266 ONLINE B Spring 2017 Assignment Section 8.6 due 04/28/2017 at 11:59pm MST 1. (1 point) Consider the function 1 1−x 3 Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms.

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Donnie Smith Sharma MAT 266 ONLINE B Spring 2017 Assignment Section 8.6 due 04/28/2017 at 11:59pm MST 1. (1 point) Consider the function 1 1−x 3 Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were ∑ ∞ n=0 3 n x 2n , you would write 1 + 3x 2 + 3 2 x 4 + 3 3 x 6 +3 4 x 8 . Also indicate the radius of convergence. Partial Sum: Radius of Convergence: Answer(s) submitted: • 1+xˆ3+xˆ6+xˆ9+xˆ12 • 1 (correct) 2. (1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = x 3 1+4x Answer: f(x) = + + + + +··· What is the interval of convergence? Answer (in interval notation): Answer(s) submitted: • (1)/(5) • (8)/(9) • (27)/(13) • (64)/(17) • (125)/(21) • 2 0 (incorrect) 3. (1 point) The function f(x) = 8 1+4x 2 is represented as a power series f(x) = ∞ ∑ n=0 cnx n . Find the first few coefficients in the power series. c0 = c1 = c2 = c3 = c4 = Find the radius of convergence R of the series. R = . Answer(s) submitted: • 8 • 0 • -32 • 0 • 128 • (1)/(2) (correct) 4. (1 point) Suppose that 6x (7+x) = ∞ ∑ n=0 cnx n . Find the first few coefficients. c0 = c1 = c2 = c3 = c4 = Find the radius of convergence R of the power series. R = . Answer(s) submitted: • • • • • • (incorrect) 5. (1 point) The function f(x) = 6 (1−2x) 2 is represented as a power series f(x) = ∞ ∑ n=0 cnx n . Find the first few coefficients in the power series. c0 = c1 = 1 c2 = c3 = c4 = Find the radius of convergence R of the series. R = . Answer(s) submitted: • • • • • • (incorrect) 6. (1 point) The function f(x) = 3x 2 (1−4x) 2 is represented as a power series f(x) = ∞ ∑ n=0 cnx n . Find the first few coefficients in the power series. c1 = c2 = c3 = c4 = c5 = Find the radius of convergence R of the series. R = . Answer(s) submitted: • 3 • 24 • 144 • 768 • 3840 • (incorrect) 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. For example, if the series were ∑ ∞ n=0 3 n x 2n , you would write 1 + 3x 2 + 3 2 x 4 + 3 3 x 6 + 3 4 x 8 . Also indicate the radius of convergence. Partial Sum: Radius of Convergence: Answer(s) submitted: • • (incorrect) 8. (1 point) The function f(x) = 8x ln(1+2x) is represented as a power series f(x) = ∞ ∑ n=0 cnx n . Find the FOLLOWING coefficients in the power series. c0 = c1 = c2 = c3 = c4 = Find the radius of convergence R of the series. R = . Answer(s) submitted: • • • • • • (incorrect) 9. (1 point) Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f(x) = ln(6−x) Answer: f(x) = + + + + +··· What is the radius of convergence? Answer: R = Answer(s) submitted: • • • • • • (incorrect) 2 10. (1 point) Consider the function arctan(x/6). Write a partial sum for the power series which represents this function consisting of the first 5 nonzero terms. For example, if the series were ∑ ∞ n=0 3 n x 2n , you would write 1 + 3x 2 + 3 2 x 4 + 3 3 x 6 +3 4 x 8 . Also indicate the radius of convergence. Partial Sum: Radius of Convergence: Answer(s) submitted: • • (incorrect) 11. (1 point) a) Consider the function arctan(x 2 ). Write a partial sum for the power series which represents this function consisting of the first 4 nonzero terms. For example, if the series were ∑ ∞ n=0 3 n x 2n , you would write 1+3x 2 +3 2 x 4 +3 3 x 6 . Also indicate the radius of convergence. Partial Sum: Radius of Convergence: b) Use part a) to write the partial sum for the power series which represents R arctan(x 2 )dx. Write the first 4 nonzero terms. Also indicate the radius of convergence. Partial Sum: Radius of Convergence: c) Use part b) to approximate the integral R 0.5 0 arctan(x 2 )dx. Answer(s) submitted: • • • • • (incorrect) Generated by c WeBWorK, http://webwork.maa.org, Mathematical Association of America 3

 
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