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Unformatted text preview: MATH 162 FALL 2006 FINAL EXAM DECEMBER 13, 2006 STUDENT NAME & ID- RECITATION TIME & INSTRUCTOR INSTRUCTIONS 1. Verify that you have 12 pages. 2. Fill in the blank spaces above. 3. Use a number 2 pencil to write on your mark-sense sheet . 4. On your mark sense sheet , write your name, your student ID number, the division and section numbers of your recitation, and fill the corresponding circles. 5. Mark the letter of your response for each question on the mark-sense sheet. 6. There are 22 questions, the first two are worth 10 points each. The others are worth 9 points each. 7. Show as much as possible of your work. Although this exam will be machine graded, in certain situations it may be necessary that we look at your exam. 8. No books, notes or calculators may be used. USEFUL FORMULAS sin 2 x = 1- cos(2 x ) 2 , cos 2 x = 1 + cos(2 x ) 2 , 1 + tan 2 x = sec 2 x cos( 3 ) = sin( 6 ) = 1 2 , cos( 6 ) = sin( 3 ) = 3 2 , cos( 4 ) = sin( 4 ) = 2 2 Volumes V = integraldisplay b a A ( x ) dx, V = integraldisplay b a 2 xf ( x ) dx Moments and center of mass M x = integraldisplay b a 1 2 ( ( f ( x )) 2- ( g ( x )) 2 ) dx, M y = integraldisplay b a x ( f...
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