MultiFinalExam01

MultiFinalExam01 - Math 2224 Practice Questions...

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Math 2224 Practice Questions Instructions: The Final Exam in this course is scheduled for Tuesday, December 11, from 1:05–3:05 pm in McB 129 (not our usual room!). There will be two review session: one in class on Tuesday, and one on Sunday, December 9, from 7:30–10:00 pm in McB 129 (the same room as the final). Here are some practice questions for the final. An answer key is included as the last page (don’t peek!) As a whole these questions emphasize computation over theory (though there are a few exceptions!) I believe with only a few days left, the benefit to be gained in terms of speed and accuracy from practicing computation will be worthwhile. You should expect the actual departmental final to be more balanced. 1. Find an equation for the plane consist- ing of all points that are equidistant from the two points ( 1, 1, 0 ) and ( 0, 1, 1 ) . (a) x - z = 0 (b) x - z = 1 (c) x - y = 0 (d) x - y = 1 (e) x + z = 1 2. Find the point at which the two lines ~ r = h 1, 1, 0 i + t h 1, - 1, 2 i and ~ r = h 2, 0, 2 i + s h- 1, 1, 0 i intersect. (a) ( 1, 0, 1 ) (b) ( 2, 0, 2 ) (c) ( 1, 1, 1 ) (d) ( 2, 2, 2 ) (e) ( 1, 1, 0 ) 3. Identify the surface 2 = y 2 + z 2 . (a) ellipsoid (b) hyperboloid of one sheet (c) hyperboloid of two sheets (d) cylinder (e) elliptic paraboloid 4. Identify the trace of the surface x = y 2 + z 2 in the plane z = 1. (a) ellipse (but not a circle) (b) parabola (c) hyperbola (d) two intersecting lines (e) circle 5. The point ( 1, 3, 2 ) is expressed in spherical coordinates as: (a) ( 2, π 6 , π 4 ) (b) ( 4, π 3 , π 4 ) (c) ( 2, π 6 , π 4 ) (d) ( 8, π 6 , π 4 ) (e) ( 8, π 3 , π 4 ) 6. Let f ( x , y ) = ( x 2 + y ) 3 . If x = 1, find f ( x , 2 x ) . (a) 3 (b) 8 (c) 9 (d) 16 (e) 27 1
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7. Find the range of the function f ( x , y ) = e x - y 2 . (a) ( 0, ) (b) [ 0, ) (c) ( 1, ) (d) [ 1, ) (e) ( - , ) 8. Evaluate lim ( x , y ) ( 1, - 1 ) x 2 - y 2 x + y (a) 0 (b) 1 (c) 2 (d) 3 (e) does not exist 9. Let f ( x , y , z ) = x yz , x > 0. Find the value of f z ( 2, 3, 0 ) . (a) 1
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This note was uploaded on 04/02/2008 for the course MATH 2224 taught by Professor Mecothren during the Fall '03 term at Virginia Tech.

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MultiFinalExam01 - Math 2224 Practice Questions...

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