Name: College ID: Thomas Edison State College Calculus II (MAT-232) Section no.: Semester and year: Written Assignment 9 Answer all assigned exercises, and show all work. Each exercise is worth 10 points. *Submitting a graph is not required; however, you are encouraged to create one for your own benefit and to include (or describe) one if possible. Section 8.6 2. Determine the radius and interval of convergence. 3k k k! x k 0 4. Determine the radius and interval of convergence. k 2 k 0 k xk 8. Determine the radius and interval of convergence. 1 k ( x 1) 2 k 1 k 1 10. Determine the radius and interval of convergence. WA 9, p. 1 1 k k 4 2 (3x 2) k 12. Determine the radius and interval of convergence. (1) k k (3x 1)k k 1 16. Determine the radius and interval of convergence. (k !)2 2 k 1 (2k )! x k 2 20. Determine the interval of convergence and the function to which the given power series converges. ( x 3) k k 0 24. Determine the interval of convergence and the function to which the given power series converges. x 3 4 k 0 WA 9, p. 2 k 26. Find a power series representation of f(x) about c = 0 (refer to example 6.6). Also, determine the radius and interval of convergence, and graph f(x) together with the partial sums and . 3 ak x k k 0 f ( x) 6 a x k 0 k k 3 x 1 28. Find a power series representation of f(x) about c = 0 (refer to example 6.6). Also, determine the radius and interval of convergence, and graph f(x) together with the partial sums and . 3 ak x k k 0 f ( x) WA 9, p. 3 2 1 x2 6 a x k 0 k k Name: College ID: Thomas Edison State College Calculus II (MAT-232) Section no.: Semester and year: Written Assignment 9 Answer all assigned exercises, and show all work. Each exercise is worth 10 points. *Submitting a graph is not required; however, you are encouraged to create one for your own benefit and to include (or describe) one if possible. Section 8.6 2. Determine the radius and interval of convergence. 3k k k! x k 0 4. Determine the radius and interval of convergence. k 2 k 0 k xk 8. Determine the radius and interval of convergence. 1 k ( x 1) 2 k 1 k 1 10. Determine the radius and interval of convergence. WA 9, p. 1 1 k k 4 2 (3 x 2)k 12. Determine the radius and interval of convergence. (1) k k (3x 1)k k 1 16. Determine the radius and interval of convergence. (k !) 2 2 k 1 (2k )! x k 2 20. Determine the interval of convergence and the function to which the given power series converges. ( x 3) k k 0 24. Determine the interval of convergence and the function to which the given power series converges. x 3 4 k 0 k 26. Find a power series representation of f(x) about c = 0 (refer to example 6.6). Also, determine the radius and interval of convergence, and graph f(x) together with the partial sums and . 3 ak x k k 0 6 a x k 0 WA 9, p. 2 k k f ( x) 3 x 1 28. Find a power series representation of f(x) about c = 0 (refer to example 6.6). Also, determine the radius and interval of convergence, and graph f(x) together with the partial sums and . 3 ak x k k 0 f ( x) 6 a x k 0 2 1 x2 WA 9, p. 3 k k