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Math 126 - TaylorHW2

Math 126 - TaylorHW2 - j x 2 j 1 2 j 1(e R = 1 10(a ∞ X j...

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Homework 2 Selected Answers Math 126 2. (b) X j =0 x 2 j +1 (2 j + 1)! , (c) X j =0 x 2 j (2 j )! . 3. (a) X k =0 x k 2 k +1 , (b) R = 2. 4. X k =1 ( - 1) k - 1 x k k . 5. X j =1 ( - 1) j - 1 x 2 j j or X j =0 ( - 1) j x 2 j +2 j + 1 . 6. (a) X k =0 ( - 1) k x k k ! , (b) same as 2b, (c) same as 2c. 7. (b) X j =0 ( - 1) j x 2 j +1 (2 j + 1) · j ! . 8. (a) X j =0 ( - 1) j x 2 j (2 j + 1)! , (b) X j =0 ( - 1) j x 2 j +1 (2 j + 1) · (2 j + 1)! . 9. (b) X j =0 ( - 1) j x 2 j , (c) R = 1, (d) X j =0 ( - 1)
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Unformatted text preview: j x 2 j +1 2 j + 1 , (e) R = 1. 10. (a) ∞ X j =0 (-1) j x 2 j +2 (2 j + 1)(2 j + 2) , (b) G ( x ) = x tan-1 x-1 2 ln(1 + x 2 ), (c) same as 10a (hint: use second form above for answer to problem 5)....
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