Final_Fall-2007-2008_1

# Final_Fall-2007-2008_1 - 1 FINAL EXAMINATION MATH 201 11:30...

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1 FINAL EXAMINATION MATH 201 January 24, 2008; 11:30 A.M.-1:30 P.M. Name: Signature: Circle Your Section Number: 17. 18 19 20 24 25 Instructions: There are two types of questions: PART I consists of six work-out problems. Give detailed solutions. PART II consists of eight multiple-choice questions each with exactly one correct answer . Circle the appropriate answer. Grading policy: 10 points for each problem of PART I . 5 points for each problem of PART II . 0 point for no, wrong, or more than one answer of PART II . GRADE OF PART I /60 GRADE OF PART II /40 TOTAL GRADE /100

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2 Part I (1). Use Lagrange Multipliers to ﬁnd the absolute maximum and minimum values for the function f ( x,y,z ) = x - y + z on the unit sphere x 2 + y 2 + z 2 - 1 = 0 .
3 Part I (2). Use cylindrical coordinates to ﬁnd the volume of the solid bounded above by the surface z = e x 2 + y 2 , below by the xy - plane, and laterally by the cylinder x 2 + y 2 = 1 .

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4 Part I (3). Find the absolute maximum and minimum values of the function
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Final_Fall-2007-2008_1 - 1 FINAL EXAMINATION MATH 201 11:30...

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