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Unformatted text preview: Expand ∑ ∞ = n n n x a Now, what happens when we take the derivative of this? Thm – If ∑ ∞ = n n n x a converges on (c, c) then ( 29 ∑ ∞ = n n n x a dx d converges on (c, c) (you still must check the endpoints for each problem) Example: Show that x x dx d cos sin = using their power functions Integration of Series: Thm – If ∑ ∞ = = ) ( n n n x a x f converges on (c, c), then ∑ ∞ = + + = 1 1 ) ( n n n x n a x g converges on (c, c) and C x g dx x f + = ∫ ) ( ) ( More examples: 1. Find a power series for x 1 tanusing integration. 2. Given 2 ( ) cos f x x x = , find ( 29 9 f . 3. Expand ln(cos( )) x in powers of x . DAILY EMCF 10 2. When taking the integral of a series, you don’t need to put +C if its indefinite. a. True b. False Final Exam Review:...
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This note was uploaded on 03/07/2012 for the course MATH 11278 taught by Professor Jeffmorgan during the Summer '10 term at University of Houston.
 Summer '10
 JEFFMORGAN

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