True/False Quizzes for
Calculus Applied to the Real World
(Chapter 8)

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1. If f(x, y) = x2 + y2 xy + 2, then f(y, x) = f(x, y).
2. If f(x, y, z) = (xy)z, then f(x, y, z) = f(y, x, z).
3. (x1)2 + (y+1)2 = 2 is the equation of the circle with center (1,1) and radius 2.
4. The function A(x, y, z) = 1 2x + 4z is a linear function.
5. The xy, yz, and xz-planes are perpendicular to each other.
6. The plane x = 1 is parallel to the yz-plane.
7. The plane x + y = 1 is parallel to the z-axis.
8. The graph of f(x, y) = [x2 + y2]1/2 is a paraboloid.
9. The graph of f(x, y) = x2 + y2 1 is obtained from the paraboloid z = x2 + y2 by dropping it one unit vertically.
10. The level curves of f(x, y) = x2 + y2 + 1 are circles.
11. Slices through the graph of f(x, y) = x2 y2 + 1 along the planes y = constant are circles.
12. The slice through the graph of f(x, y) = x2 y2 + 1 along the plane x = y is a straight line.
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.
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.
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.
16. 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. 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. The average of f on a rectangle is the average of its values at the four corners.
19. To find the total population, integrate the population density over the region in question.
20. To integrate over any region, we may evaluate the iterated integral in either order.

Last Updated: August, 1999
Copyright © 1999 Stefan Waner & Steven R. Costenoble