# WA5(1).docx - Calculus II(MAT-232 Semester and year June...

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Calculus II (MAT-232) Semester and year: June 2019 Written Assignment 5 Answer all assigned exercises, and show all work. Each exercise is worth 5 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 4. Determine the radius and interval of convergence. 0 2 k k k k x 1 0 1 1 2 lim 2 ( 1) 1 lim lim 2 2 1 lim 1 1 2 1 1 1 2 2 1; 2; 2 2 2 2 1; 2; 2 2 2 2 2 2 ( 2) _ _ _ 2 2 2 k k k k k k k k k k k k x k x x e k x k k k k x x g k x x x x x x x x k forx diver es by alternating ser x i               0 _ 2 (2) _ _ _ _ 2 2 ( 2,2) k k k s test k forx diverges by Test For Divergence radius Internal   WA 5, p. 1
10. Determine the radius and interval of convergence. 2 4 1 (3 2) k k x k 1 1 2 2 2 2 2 1 2 2 2 2 2 2 4 3 2 1 3 2 1 1 lim 1 (3 2) 3 2 (3 2) (3 2) lim 3 2 lim 3 2 1 3 2 ( 1) ( 1 1 1 3 2 1 3 3 1 1 1 3 ) 1 3 2 1 (3 1 : 3 2) k k k k k k k k k k k x x k k x x k k k x k x k x x x x x x f x k k k x or k x           2 4 _ _ _ _ 1 1: (3 2) _ _ _ 1 3 1 [ 1, ] 3 k k converges by P Series Test forx x converges Alternating Series Test k radius Interval    WA 5, p. 2
12. Determine the radius and interval of convergence. 1 ( 1) (3 1) k k k x k 1 1 1 1 1 3 1 1 3 1 3 1 3 1 (3 1) 1 1 lim 1 1 (3 1) 1 (3 1) 1 1 (3 1) 3 1 (3 1 1 ) lim 3 1 lim 3 1 3 1 1 3 1 1 1 3 1 1 1 1 3 1 1 1 k k k k k k k k k k k k k x x x x k k x k k x k x k k x x k k k k x x k x x x x x k k         1 lim _ _ _ _ _ ( 1) l ] 3 i 1 1 0 3 2 0 2 3 3 3 2 0 3 0 : 0 : 1 3 2 (0, 3 m _ _ _ _ _ k k k x x diverges pe t r P Series Test k converges per Alternating a e x Forx Fo Seri s Te rx radius In erv ts k l     WA 5, p. 3
16. Determine the radius and interval of convergence.