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Test 1-SP07

# Test 1-SP07 - Phys 208 Theoretical Physics Test 1(Feb 2...

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Phys 208 – Theoretical Physics – Test 1 (Feb. 2, 2007) 1.(15 pts) Find the interval of convergence for the following power series. Be sure to check the endpoints of the interval. 1 ( 1) ( 1) n n n x n = + 2. (20 pts) Recall the binomial series is defined as 2 3 0 ( 1) ( 1)( 2) (1 ) 1 2! 3! p n n p p p p p p x x px x x n = + = = + + + + " where p is any real number, positive or negative. Find the Maclaurin series for a function defined by the following integral: 2 0 ( ) 1 x dt f x t = a) Give the general series. b) What are the first three terms? 3. (10 pts) Evaluate the complex number,
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