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FINAL REVIEW #2-problems

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

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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 10.0points 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 10.0points 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 10.0points 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 10.0points 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

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suleimenov (bs26835) – FINAL REVIEW #2 – rusin – (55565) 2 005 10.0points Find a power series representation for the function f ( y ) = ln radicalbigg 1 + 3 y 1 3 y .
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