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Gilbert_ReviewFinal - moseley(cmm3869 FinalREVIEW...

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moseley (cmm3869) – FinalREVIEW – Gilbert – (56380) 1 This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the value of lim x 2 ln( x 2 3) 4 x 8 . 1. limit = 5 4 2. limit does not exist 3. limit = 1 4. limit = 1 4 5. limit = 1 2 6. limit = 3 2 002 10.0 points Determine if the improper integral I = integraldisplay 1 0 4 sin - 1 x 1 x 2 dx is convergent or divergent, and if convergent, find its value. 1. I is divergent 2. I = 1 2 π 2 3. I = 1 4 4. I = 1 4 π 2 5. I = 1 2 003 10.0 points Determine if the sequence { a n } converges when a n = (2 n 1)! (2 n + 1)! , and if it converges, find the limit. 1. does not converge 2. converges with limit = 0 3. converges with limit = 1 4. converges with limit = 4 5. converges with limit = 1 4 004 10.0 points Let f be a continuous, positive, decreasing function on [5 , ). Compare the values of the integral A = integraldisplay 18 5 f ( z ) dz and the series B = 18 summationdisplay n =6 f ( n ) . 1. A = B 2. A > B 3. A < B 005 10.0 points Determine the interval of convergence of the series summationdisplay n =1 n 2 n ( x 5) n . 1. interval convergence = [ 3 , 7 ] 2. interval convergence = [ 2 , 5 ]
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moseley (cmm3869) – FinalREVIEW – Gilbert – (56380) 2 3. interval convergence = ( 2 , 5 ) 4. interval convergence = [ 3 , 7 ) 5. interval convergence = [ 2 , 5 ) 6. interval convergence = ( 3 , 7 ) 006 10.0 points Find a power series representation centered at the origin for the function f ( y ) = 1 (3 y ) 2 . 1. f ( y ) = summationdisplay n =1 n 3 n +1 y n - 1 2. f ( y ) = summationdisplay n =0 n + 1 3 n y n 3. f ( y ) = summationdisplay n =1 1 3 n +1 y n 4. f ( y ) = summationdisplay n =0 ( n + 1) y n 5. f ( y ) = summationdisplay n =1 n 3 n y n - 1 6. f ( y ) = summationdisplay n =0 1 3 n +1 y n 007 10.0 points Compute the degree 2 Taylor polynomial for f centered at x = 1 when f ( x ) = x .
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