# Exam 3 - Version 057 – Exam03 – Gilbert – (56380) 1...

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Unformatted text preview: Version 057 – Exam03 – Gilbert – (56380) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points From the contour map of f shown below de- cide whether f x and f y are positive, negative, or zero at P . 2 2 4 4 6 6 P x y 1. f x = 0 , f y > 2. f x < , f y < 3. f x = 0 , f y < 4. f x > , f y < 5. f x < , f y > correct 6. f x > , f y > Explanation: When we walk in the x-direction from P we are walking downhill, so f x < 0. On the other hand, when we walk in the y-direction from P we are walking uphill, so f y > 0. Consequently, at P f x < , f y > . keywords: contour map, contours, partial derivative, slope, 002 10.0 points Which equation has the surface x y z as its graph in the first octant? 1. x 3 + y 5 + z 4 = 1 2. x 5 + y 3 + z 4 = 1 correct 3. x 5 + y 4 + z 3 = 1 4. x 3 + y 4 + z 5 = 1 5. x 4 + y 5 + z 3 = 1 6. x 4 + y 3 + z 5 = 1 Explanation: As the surface is a plane, it must be the graph of a linear function which can be writ- ten in intercept form as x a + y b + z c = 1 . But by inspection we see that the x-intercept is x = 5, the y-intercept is y = 3 and the z- intercept is z = 4. Consequently, the surface is the graph in the first octant of the equation x 5 + y 3 + z 4 = 1 . Version 057 – Exam03 – Gilbert – (56380) 2 003 10.0 points Which one of the following equations has graph 1. x + z 2 − 4 = 0 2. z + y 2 − 4 = 0 3. y − z 2 + 4 = 0 4. x − y 2 + 4 = 0 5. z − x 2 + 4 = 0 correct Explanation: The graph is a parabolic cylinder that has constant value on any line parallel to the y- axis, so it will be the graph of an equation containing no y-term. This already eliminates the equations x − y 2 + 4 = 0 , y + x 2 − 4 = 0 , y − z 2 + 4 = 0 , z + y 2 − 4 = 0 . On the other hand, the intersection of the graph with the xz-plane, i.e. the y = 0 plane, is a parabola opening upwards on the z-axis as shown in x z Consequently, the graph is that of the equa- tion z − x 2 + 4 = 0 ....
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## This note was uploaded on 09/27/2010 for the course M 408 D taught by Professor Textbookanswers during the Spring '07 term at University of Texas.

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Exam 3 - Version 057 – Exam03 – Gilbert – (56380) 1...

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