Test1-FS04 - Phys 208 Theoretical Physics Test 1 ( Sept....

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Phys 208 – Theoretical Physics – Test 1 ( Sept. 29, 2004) 1. (20 pts) Find the interval of convergence for the following power series; be sure to investigate the endpoints of the interval. () = 1 2 2 32 1 nn n x n 2. (20 pts) Recall the binomial series is , ! ( ) ! 11 1 2 12 3 23 += + + + − − + xp x pp x p x p " where p is any real number, positive or negative. Find the Maclaurin series for the function defined by the following integral. . Hint: Multiply (or divide) the sine series by an fx t t dt x sin = 1 2 0 appropriate series and integrate the first three terms. 3. (20 pts.) Find the roots of . You can leave the roots in polar form. 16 4 i 4. (20 pts) Evaluate in Cartesian form, . 2 1 i i +
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