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Quiz 3 Practice Problems - Calculus III | MATH 215, Quizzes of Advanced Calculus

University of Michigan (UM) - Ann ArborAdvanced Calculus

Material Type: Quiz; Class: Calculus III; Subject: Mathematics; University: University of Michigan - Ann Arbor; Term: Winter 2004;

Typology: Quizzes

Pre 2010

Uploaded on 09/02/2009

koofers-user-80
koofers-user-80 🇺🇸

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Math 215-060 Quiz 3 Name: February 5, 2004
Problem 1. (5 pts.) Suppose that the following table gives values of a function f(x, y). Use this to sketch a
contour map showing the level curves of the function. Include and label the contours with values −2,−1,0,1,2,
4and 6.x =
0 1 2 3
3 0 -2 -2 0
y= 2 0 -1 0 3
1 0 0 2 6
0 0 1 4 9
Problem 2. (5 pts.) Find the plane tangent to the function g(x, y) = 3xcos(x−y)at the point (2,2 + π). Then
find a vector normal to the tangent plane.

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Math 215-060 Quiz 3 Name: February 5, 2004

Problem 1. (5 pts.) Suppose that the following table gives values of a function f (x, y). Use this to sketch a contour map showing the level curves of the function. Include and label the contours with values − 2 , − 1 , 0 , 1 , 2 , 4 and 6. x = 0 1 2 3 3 0 -2 -2 0 y= 2 0 -1 0 3 1 0 0 2 6 0 0 1 4 9

Problem 2. (5 pts.) Find the plane tangent to the function g(x, y) = 3x cos(x − y) at the point (2, 2 + π). Then find a vector normal to the tangent plane.