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Unformatted text preview: f described above. b. Estimate the accuracy with which this 7th Taylor polynomial approximates 4 1 f . 4. (25) a. Determine which series converge and which diverge. Be sure to tell which convergence test you are using. i. ∑ ∞ = + 1 ! 5 1 k k k k ii. ∑ ∞ =1 ) sin( 3 k k k iii. ∑ ∞ = +1 ) ln( ) 1 ( ) 1 ( k k k k b. Calculate the radius of convergence of ( 29 ∑ ∞ = +1 1 8 3 2 ) 1 ( k k k k k x k Name Page 3 of 3 Math 1502J Andrew Hour Test 1 Teaching Assistant 11 February 2010 ANSWERS 1. a. x x e e y 2 3 6 + = b. C x y += 3 3 1 1 2. a. 2 b. Converges to 2 1 3. a. ( 29 6 4 2 7 ! 5 1 ! 3 1 1 x x x x P+= b. ( 29 ( 29 ! 7 4 1 8 4. a. i. Converges by the Ratio Test ii. Diverges by the basic comparison test, compare to ∑ k 1 iii. Converges by the Alternating Series Test b. 2 3 = R...
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 Spring '08
 Morley
 Calculus, Mathematical Series, Andrew Teaching Assistant, Math 1502J Andrew, 1502J Andrew Teaching

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