| 1. |
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If f(x, y) = x2 + y2  xy + 2, then f(y, x) = f(x, y). |
| 2. |
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If f(x, y, z) = (xy)z, then f(x, y, z) = f(y, x, z). |
| 3. |
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(x1)2 + (y+1)2 = 2 is the equation of the circle with center (1,1) and radius 2. |
| 4. |
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The function A(x, y, z) = 1 2x + 4z is a linear function. |
| 5. |
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The xy, yz, and xz-planes are perpendicular to each other. |
| 6. |
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The plane x = 1 is parallel to the yz-plane. |
| 7. |
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The plane x + y = 1 is parallel to the z-axis. |
| 8. |
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The graph of f(x, y) = [x2 + y2]1/2 is a paraboloid. |
| 9. |
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The graph of f(x, y) = x2 + y2 1 is obtained from the paraboloid z = x2 + y2 by dropping it one unit vertically. |
| 10. |
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The level curves of f(x, y) = x2 + y2 + 1 are circles. |
| 11. |
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Slices through the graph of f(x, y) = x2 y2 + 1 along the planes y = constant are circles. |
| 12. |
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The slice through the graph of f(x, y) = x2 y2 + 1 along the plane x = y is a straight line. |
| 13. |
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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. |
| 14. |
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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. |
| 15. |
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| 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. |
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| 16. |
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The least squares (regression) line associated with the two points (p1, q1), (p2, q2), p1  p2, is always the same as the straight line passing through those points. |
| 17. |
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The least squares (regression) line associated with the three points (p1, q1), (p2,q2), (p3, q3), p1 < p2 < p3, must pass through at least one of the points. |
| 18. |
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The average of f on a rectangle is the average of its values at the four corners. |
| 19. |
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To find the total population, integrate the population density over the region in question. |
| 20. |
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To integrate over any region, we may evaluate the iterated integral in either order. |
