22t2f07aweb

22t2f07aweb - Math 22 - Calculus of Several Variables M....

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Math 22 - Calculus of Several Variables Exam 2 - Chapter 14 M. Eastman - Fall 2007 1. Given : 0ÐBßCÑœ B C * È ## a. Sketch the the domain, and state the range of . 0 b. Sketch the level curves and . Label each level curve 0ÐBßCÑ œ ! 0ÐBßCÑ œ #( È clearly. c. Find the equation of the tangent plane to the surface when and . Write Bœ % Cœ$ your answer in the form +B,C-D.œ!Þ 2. Given , find: 0ÐBßCÑ œ -9= B *C / ab #B C $ # a. b. c. d. 0 ÐBß CÑ 0 ÐBß CÑ 0 ÐBß CÑ f0 $ß  " BB B C B e. the directional derivative of at in the direction of the point . 0$ ß " Ð & ß ! Ñ 3. If , and if changes from to , find: D œ 0ÐBß CÑ œ B  &BC  C ÐBß CÑ Ð#ß $Ñ Ð"Þ*ß $Þ!&Ñ $# a. (the actual change in ) b. (the total differential of ? DD . D D Ñ 4. Given the function where and X œ68 B C D Bœ:$;ß Cœ$:;ß Dœ$:;ß ### use the chain rule to find and when and . Show your work. `X `: `; :œ # ;œ" 5. Find the critical points for . Find the value of at each 0 Ð B ßC ÑœBCBC" ! B 0 # # critical point, the value of
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22t2f07aweb - Math 22 - Calculus of Several Variables M....

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