e306k

# e306k - Exam III and Key MAC 2312 April 3, 2006 S Hudson 1)...

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Exam III and Key April 3, 2006 MAC 2312 S Hudson 1) (5pt each) Compute (or state that it diverges): a) R x 2 +1 x - 1 dx b) R + 0 e 2 x dx c) R 1 0 dx 1 - x 2 d) R x 2 ( x +3) 3 dx 2) (5pt each) Compute (or state that it diverges): a) k =1 ( - 3 / 4) k - 1 b) k =1 1 ( k +2)( k +3) 3) (10pt) Find the general term a k of this sequence, and its limit L . 1 , - 1 / 2 , 1 / 3 , - 1 / 4 , 1 / 5 . . . 4) (10pt) Show that { 2 n 2 - 7 n } is eventually monotone. 5) (10pt) Compute R dx x 2 - 4 x +5 6) (5pt each) State whether the series converges or diverges, with a brief reason (eg a theorem or a test): a) k =3 1 k b) k =1 k 2 2 k 2 +1 c) k =3 ( - 1) k 2 k +1 d) k =1 1 k ln( k ) 7) (10pts) Use the Trapezoid Rule to approximate R 2 1 x 2 dx with n = 2. 1

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Based on your knowledge of y = x 2 (increasing, concave up, etc), and perhaps a picture, explain whether this approximation is too large or too small. 8) (10pts) Choose ONE, and explain thoroughly:
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## This note was uploaded on 12/26/2011 for the course MAC 2312 taught by Professor Storfer during the Summer '08 term at FIU.

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e306k - Exam III and Key MAC 2312 April 3, 2006 S Hudson 1)...

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