samples2934

# samples2934 - Arkansas Tech University MATH 2934(Dr Finan...

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Arkansas Tech University MATH 2934 (Dr. Finan) Exam # 1 (Spring 2007) P.S: In order to get partial credits you must show your work. Good Luck. Exercise 1 (10 points) Which of the three points P 1 = (1 , 2 , 3) ,P 2 = (3 , 2 , 1) and P 3 = (1 , 1 , 0) are closest to each other? Justify your answer. Exercise 2 (10 points) By setting one variable constant, ±nd a plane that intersects the surface z =4 x 2 - y 2 + 1 in a: (a) Parabola opening upward (b) Parabola opening downward (c) Pair of intersecting straight lines. Exercise 3 (10 points) Sketch a contour diagram of z = f ( x, y )= - x 2 - y 2 + 1 using the values z = - 2 and z = ± 1 . Exercise 4 (10 points) Find a formula of a plane passing through the point (4 , 3 , - 2) and with slope 5 in the x - direction and slope - 3 in the y - direction. Exercise 5 (10 points) Write the level surface x +2 y +3 z = 5 as the graph of a function f ( x, y ) of two variables. Exercise 6 (10 points) Show that lim ( x,y ) (0 , 0) x 2 y x 4 + y 2 does not exist. Exercise 7 (10 points) What value of c make the following function continuous at (0 , 0)? f ( x, y ± x 2 + y 2 + 1 ( x, y ) ² = (0 , 0) c ( x, y ) = (0 , 0)

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Exercise 8 (10 points) Find a formula for a function f ( x, y, z ) whose level surface f = 4 is a sphere of radius 2 centered at (0 , 0 , 0) . Exercise 9 (10 points) Graph the linear function z = 4 + x - 2 y. Exercise 10 (10 points) Consider the Cobb-Douglas production function P ( L, K )=1 . 01 L 0 . 75 K 0 . 25 . What is the e±ect on production of doubling both labor and capital?
Arkansas Tech University MATH 2934 (Dr. Finan) Exam # 2 (Spring 2007) P.S: In order to get partial credits you must show your work. Good Luck. Exercise 1 (10 points) Consider the vector "v =5 " i - 7 " j. (a) Find the angle between this vector and the positive x - axis.

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## This note was uploaded on 10/21/2009 for the course MATH 223 taught by Professor Punosevac during the Spring '08 term at Arizona.

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samples2934 - Arkansas Tech University MATH 2934(Dr Finan...

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