22t2s08aweb

# 22t2s08aweb - Math 22 - Calculus of Several Variables M....

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Math 22 - Calculus of Several Variables Midterm 2 - Form A M. Eastman - Spring 2008 1. Given : 0ÐBßCÑ œ \$ C B È # a. Sketch the the domain, and state the range of . 0 b. Sketch the level curves and . Label each level curve clearly. 0ÐBßCÑ œ ! 0ÐBßCÑ œ # 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: 0ÐBßCÑœ=38 #C B 68 B &C ab ## a. 0CÐBßCÑ b. B ß C Ñ CC c. B ß C Ñ BC d. f0 #ß  " e. the directional derivative of at in the direction of the point . 0# ß " Ð ! ß " Ñ 3. Given , where and use the chain rule to find D œ B † =38 C B œ @ † -9= A C œ À \$ A` D @` @ and when and `D `A @œ% Aœ Þ 1 4. Find the critical points for . Find the value of at 0ÐBß CÑ œ B  BC  \$C  #B  #% 0 ### each critical point, and classify the function value at each critical point as either a (local) maximum, (local) minimum, or a saddle point. The number of lines in the table do not necessarily indicate the number of points. Justify your answers.

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## This note was uploaded on 10/10/2009 for the course MATH 22 taught by Professor Castro during the Spring '08 term at UCSC.

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22t2s08aweb - Math 22 - Calculus of Several Variables M....

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