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Unformatted text preview: 8 ≤ x f for all x , 2 1 ≤ ≤ x . a. Find the 7th Taylor polynomial at 0 for the function f described above. b. Estimate the accuracy with which this 7th Taylor polynomial approximates 2 1 f 4. (25) a. Determine which series converge and which diverge. Be sure to tell which convergence test you are using. i. ∑ ∞ = 1 2 ! k k k ii. ∑ ∞ = + 1 2 3 ) cos( 2 k k k iii. ∑ ∞ = + 1 2 2 ) 1 ( k k k k b. Calculate the radius of convergence of ( 29 ∑ ∞ =1 2 3 ) 1 ( k k k k x k Name Page 3 of 3 Math 1502 E Andrew Hour Test 1 Teaching Assistant 11 February 2010 ANSWERS 1. a. x x e C e x y 3 3+ = b. 1 1 2= x y 2. a. 0 b. Converges to 2 1 3. a. ( 29 6 4 2 7 ! 5 1 ! 3 1 x x x x P += b. ( 29 ( 29 8 2 ! 7 1 4. a. Diverges by the Basic divergence test, terms do not tend to 0. b. Converges by the Ratio Test c. 3 = R...
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 Spring '08
 Morley
 Calculus, Andrew Teaching Assistant

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