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Unformatted text preview: radius of convergence ( a ) 3 (1 + x ) 2 ( b ) Z 1 1x 8 dx 5. (14 pts.) Find the Taylor series of f ( x ) = ln( x ) around a = 2. Give your answer in summation notation. 6. (10 pts.) Find the 3rd Taylor polynomial, T 3 ( x ), of f ( x ) = √ x around a = 9. EXAM CONTINUES ON REVERSE 7. (12 pts.) Use the Alternating Series Estimation Theorem or Taylor’s Inequality to estimate ln(1 . 1) to within an error of 0 . 001. Write your answer as a single number. ln(1 + x ) = ∞ X n =1 (1) n +1 x n n 8. (12 pts.) Use the table on the front to ﬁnd the sum of each of the following series ( a ) ∞ X n =0 (1) n π 2 n +1 6 2 n +1 (2 n + 1)! ( b ) ∞ X n =0 1 3 n n !...
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This test prep was uploaded on 03/26/2008 for the course MATH 12 taught by Professor Garant during the Spring '08 term at Tufts.
 Spring '08
 GARANT
 Math

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