Sample problems for midterm 1

Sample problems for midterm 1 - 1 ( n n n n 6.) (8.5) Find...

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15 Math 253 Sample problems for midterm 1 1. (8.1) Determine whether the sequence converges or diverges. If it converges, find the limit. a) 1 1 ) 1 ( 3 2 n n n n a n n b) 1 1 3 3 3 n n n n a n c) 1 ) sin( 3 n n n a n d) 1 2 3 n n a n n e) n n a n 3 )) (ln( f) n n n n n n a 3 * 23 5 5 * 32 4 3 2. (8.1) Determine whether the sequence is decreasing, increasing or not monotonic. Is this sequence bounded? Is this sequence convergent? If it is convergent find its limit. a) n n n a 4 3 b) 2 / 1 1 1 n n a a a c) n n a a a / 2 1 1 1 3. (8.2)Find at least 6 partial sums of the series. Determine whether the series is convergent or divergent. If it is convergent, find its sum. For c) use telescoping sum. a) 1 1 5 4 n n n b) 1 5 4 3 * 2 2 n n n n n c) 1 2 2 3 1 n n n
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4.) (8.3) Determine whether the series is convergent or divergent. a) 1 3 2 2 3 n n n b) 1 3 2 ) cos( ) 1 ( 3 n n n n 5.) (8.4) Determine whether the series is convergent or divergent. Determine whether the series is absolute convergent. a) 1 3 2 2 3 ) 1 ( n n n n b) 1 2 2 3 )
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Unformatted text preview: 1 ( n n n n 6.) (8.5) Find the radius of convergence and interval of convergence of the series. a) 1 3 2 ) 1 3 ( n n n x b) 1 1 1 5 ) 2 ( n n n n x 7.)(8.6) Find a power representation for the function and determine the interval of convergence a) 2 3 ) ( 3 x x x f b) ) 5 2 ln( ) ( x x f 8.)(8.6)Evaluate the integral as an infinite power series. What is the radius f convergence? 2 1 ) ln( x x 9)(8.7)Find the Maclaurin series of the given function. Use this series to compute ) ( 6 f . 6 3 1 ) ( x x x e x f x 10) (8.7) Use series to evaluate the limit: 2 2 2 2 1 lim x x x e x x 11.)Use the binomial Series to expand the function as a power series. State the radius of convergence. 6 4 4 2 ) ( x x x x f...
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This note was uploaded on 08/17/2009 for the course MATH 253 taught by Professor Poplicher during the Spring '08 term at University of Cincinnati.

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Sample problems for midterm 1 - 1 ( n n n n 6.) (8.5) Find...

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