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MultiFinalExam06 - Math 2224 Common Exam FORM A Fall 2003...

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Math 2224 Common Exam Fall 2003 FORM A Instructions: Please enter your NAME, your ID NUMBER, the FORM DESIGNATION LETTER and your CRN NUMBER on the op-scan sheet. The index number should be written in the upper right-hand box labeled ”Course”. Darken the appropriate circles below the ID number and form designation letter. Use a No. 2 pencil; machine grading may ignore faintly marked circles. Mark your answers to the test questions in rows 1- 14 of the op-scan sheet. Your score on this part of the test will be the number of correct answers. You have one hour to complete this part of the final exam. 1
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[1] The linearization of f ( x, y, z ) = x 2 + e xy + yz 3 at (0 , 1 , 1) is 1) 3 x + 2 z - y + 1 2) - 2 + x + y + 3 z 3) - 2 - x + y + 3 z 4) 2 - x - y - 3 z = 0 [2] The limit lim ( x,y ) (0 , 0) 2 x 2 - y 2 2 x 2 + y 2 is 1) 1 2) 1 3 3) - 1 4) Does not exist [3] The direction in which f ( x, y ) = 2 xy - y 2 + 3 x 2 has a maximum rate of change at (2 , - 1) is 1) 10 ~ i + 6 ~ j 2) - 10 ~ i - 6 ~ j 3) 10 ~ i - 6 ~ j 4) 2 34 [4] The contour map for f ( x, y ) = x 2 - 4 y 2 consists of 1) Ellipses only
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