FINAL REVIEW #2-problems

FINAL REVIEW #2-problems - suleimenov (bs26835) – FINAL...

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Unformatted text preview: suleimenov (bs26835) – FINAL REVIEW #2 – rusin – (55565) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. More of the final review. 001 10.0 points Find the interval of convergence of the se- ries ∞ summationdisplay n =1 x n √ n + 4 . 1. converges only at x = 0 2. interval of cgce = [ − 1 , 1] 3. interval of cgce = [ − 1 , 1) 4. interval of cgce = ( − 4 , 4] 5. interval of cgce = ( − 1 , 1) 6. interval of cgce = [ − 4 , 4] 002 10.0 points Determine the interval of convergence of the series ∞ summationdisplay k = 1 ( − 1) k- 1 1 k 2 ( x − 1) k . 1. interval of convergence = [ − 2 , 0 ) 2. interval of convergence = (0 , 2 ) 3. interval of convergence = [0 , 2 ] 4. interval of convergence = (0 , 2 ] 5. interval of convergence = [0 , 2 ) 6. interval of convergence = ( − 2 , 0 ] 7. interval of convergence = [ − 2 , 0 ] 8. interval of convergence = ( − 2 , 0 ) 003 10.0 points If the radius of convergence of the power series ∞ summationdisplay n =0 c n x n is 36, what is the radius of convergence, R , of the power series ∞ summationdisplay n =0 c n x 2 n ? 1. R = 6 2. R = ∞ 3. R = 36 4. R = 0 5. R = 1 6. R = √ 6 004 10.0 points Determine the value of f (1) when f ( x ) = x 2 2 − 2 x 3 2 4 + 3 x 5 2 6 + . . . . ( Hint : differentiate the power series expan- sion of ( x 2 + 2 2 )- 1 .) 1. f (1) = 4 25 2. f (1) = 8 25 3. f (1) = 1 5 4. f (1) = 8 5 5. f (1) = 1 25 suleimenov (bs26835) – FINAL REVIEW #2 – rusin – (55565) 2 005 10.0 points Find a power series representation for the function f ( y ) = ln radicalbigg...
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This note was uploaded on 09/15/2011 for the course M 55565 taught by Professor Rusin during the Spring '11 term at University of Texas at Austin.

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FINAL REVIEW #2-problems - suleimenov (bs26835) – FINAL...

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