samples2934

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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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?
Background image of page 2
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.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 10

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online