 | Chapter 7 True/False Quiz | | Chapter 8 Summary | | Return to Quiz Index | | Return to Main Page |
Functions of Several Variables
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| Chapter 7 True/False Quiz | | Chapter 8 Summary | | Return to Quiz Index | | Return to Main Page |
1. If f(x, y) = x2 + y2 
xy + 2, then f(y, x) = f(x, y). 
True 
False
2. If f(x, y, z) = (xy)z, then f(x, y, z) = f(y, x, z). True False
3. (x1)2 + (y+1)2 = 2 is the equation of the circle with center (1,1) and radius 2. True False
4. The function A(x, y, z) = 1 2x + 4z is a linear function. True False
5. The xy, yz, and xz-planes are perpendicular to each other. True False
6. The plane x = 1 is parallel to the yz-plane and passes through the x-axis at x = 1. True False
7. The plane x + y = 1 is parallel to the z-axis. True False
8. The graph of f(x, y) = [x2 + y2]1/2 is a paraboloid. True False
9. The graph of f(x, y) = x2 + y2 1 is obtained from the paraboloid z = x2 + y2 by dropping it one unit vertically. True False
10. The level curves of f(x, y) = x2 + y2 + 1 are circles. True False
11. Slices through the graph of f(x, y) = x2 y2 + 1 along the planes y = constant are circles. True False
12. The slice through the graph of f(x, y) = x2 y2 + 1 along the plane x = y is a straight line. True False
13. If fx(a, b) = 0 and fy(a, b) > 0, then f may have a local minimum at the interior point (a, b) in its domain. True False
14. f(x, y) may have a local extremum on a boundary point (a, b) of the domain of f even if (a, b) is not a critical point. True False
15. If the second derivative test fails at some interior point of the domain of f, then f cannot have a local extremum at that point. True False
16. The least squares line associated with the two points (p1,q1), (p2,q2), p1 
p2 is necessarily the unique straight line passing through those points. True False
17. The least squares line associated with the three points (p1,q1), (p2,q2), (p3,q3), p1 < p2 < p3 must pass through at least one of those points. True False
18. The average of f on a rectangle is the average of its values at the four corners. True False
19. To find the total population, integrate the population density over the region in question. True False
20. To integrate over any region, we may evaluate the iterated integral in either order. True False