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3. (True/False) Let f(x, y) be any function of r and y. Then fofo sin(f(x, y)) dxdy ≤ 7. 4. (True/False) Every point (r, y, z) can be uniquely represented as a point (r, 0, 2) in cylindrical coordinates. 5. (True/False) If f(x, y, z)= 1, then fffy f(x, y, z)dV gives the volume of V. 6. (True/False) Let C be a closed curve. Then for a continuous function f, we have fe f ds = 0. 7. (True/False) Suppose the work done by a force F on a particle moving along a path C is given by z, then if the object moves along the path in the opposite direction (that is, along -C) the work done by F on the particle will be -z. 8. (True/False) Let F = Pi+Qj on an open region D. Suppose Py = Q. Then Fis conservative. 9. (True/False) If F is a conservative vector field, then V x F = 0. 10. (True/False) Suppose D is a region where any two points in D can be joined by a curve that stays inside D. Then D is simply connected.

3. (True/False) Let f(x, y) be any function of r and y. Then fofo sin(f(x, y)) dxdy ≤ 7. 4. (True/False) Every point (r, y, z) can be uniquely represented as a point (r, 0, 2) in cylindrical coordinates. 5. (True/False) If f(x, y, z)= 1, then fffy f(x, y, z)dV gives the volume of V. 6. (True/False) Let C be a closed curve. Then for a continuous function f, we have fe f ds = 0. 7. (True/False) Suppose the work done by a force F on a particle moving along a path C is given by z, then if the object moves along the path in the opposite direction (that is, along -C) the work done by F on the particle will be -z. 8. (True/False) Let F = Pi+Qj on an open region D. Suppose Py = Q. Then Fis conservative. 9. (True/False) If F is a conservative vector field, then V x F = 0. 10. (True/False) Suppose D is a region where any two points in D can be joined by a curve that stays inside D. Then D is simply connected.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. (True/False) Let f(x, y) be any function of a and y. Then f f sin(f(x, y)) drdy ≤7. 4. (True/False) Every point (x, y, z) can be uniquely represented as a point (r, 0, 2) in cylindrical coordinates. 5. (True/False) If f(x, y, z)= 1, then fffy f(x, y, z)dV gives the volume of V. 6. (True/False) Let C be a closed curve. Then for a continuous function f, we have fe f ds = 0. 7. (True/False) Suppose the work done by a force F on a particle moving along a path C is given by a, then if the object moves along the path in the opposite direction (that is, along -C) the work done by F on the particle will be -. 8. (True/False) Let F = P7+Q7 on an open region D. Suppose P, Q. Then F is conservative. 9. (True/False) If F is a conservative vector field, then V x = 0. 10. (True/False) Suppose D is a region where any two points in D can be joined by a curve that stays inside D. Then D is simply connected.
Transcribed Image Text:3. (True/False) Let f(x, y) be any function of a and y. Then f f sin(f(x, y)) drdy ≤7. 4. (True/False) Every point (x, y, z) can be uniquely represented as a point (r, 0, 2) in cylindrical coordinates. 5. (True/False) If f(x, y, z)= 1, then fffy f(x, y, z)dV gives the volume of V. 6. (True/False) Let C be a closed curve. Then for a continuous function f, we have fe f ds = 0. 7. (True/False) Suppose the work done by a force F on a particle moving along a path C is given by a, then if the object moves along the path in the opposite direction (that is, along -C) the work done by F on the particle will be -. 8. (True/False) Let F = P7+Q7 on an open region D. Suppose P, Q. Then F is conservative. 9. (True/False) If F is a conservative vector field, then V x = 0. 10. (True/False) Suppose D is a region where any two points in D can be joined by a curve that stays inside D. Then D is simply connected.
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