solve rest aftr 5

(1 point) IMPORTANT: You only get one try at this entire multi-response problem. Put a response in every box before choosing "Submit". Decide if each statement is True or False. Indicate your answer by entering "1" for True and "O" for False. 0 If F is a vector field, then div F is a vector field. If F is a vector field, then curl F is a vector field. If f is a smooth scalar field, then div(curl V/) = 0. O For any circle C in 3D and any smooth function f, one has VfL = 0. Given any region of 3D space and any vector field F satisfying V x F = 0 in that region, there must exist some scalar-valued function f satisfying the identity F = -Vf throughout the given region. Whenever F and Gare vector fields satisfying div F = div G at all points in space, the difference G-F is a constant vector. curl (F + G) = curl(F) + curlG). curl (FG) = curl(F). curlG. For any constant vector field F and spherical shell S, one has = 0. There exists a vector field F satisfying V F = (x, y, z). The magnetic flux dS equals o Wb exactly, for every closed surface S in space. For any circle C in 3D and any smooth vector field F, one has F. dL = 0. There exists a smooth function f satisfying the identity Vf = (1 xy) ea, + (e + x2 ery) ay. The vector-valued integral as equals 0 for every closed surface S in space. By carefully selecting a smooth function F and closed surface S, one can arrange F) .dS = 48. REMEMBER: All your responses will be checked at the same time, and there is a limit of one submission per student (no second chances!). (1 point) IMPORTANT: You only get one try at this entire multi-response problem. Put a response in every box before choosing "Submit". Decide if each statement is True or False. Indicate your answer by entering "1" for True and "O" for False. 0 If F is a vector field, then div F is a vector field. If F is a vector field, then curl F is a vector field. If f is a smooth scalar field, then div(curl V/) = 0. O For any circle C in 3D and any smooth function f, one has VfL = 0. Given any region of 3D space and any vector field F satisfying V x F = 0 in that region, there must exist some scalar-valued function f satisfying the identity F = -Vf throughout the given region. Whenever F and Gare vector fields satisfying div F = div G at all points in space, the difference G-F is a constant vector. curl (F + G) = curl(F) + curlG). curl (FG) = curl(F). curlG. For any constant vector field F and spherical shell S, one has = 0. There exists a vector field F satisfying V F = (x, y, z). The magnetic flux dS equals o Wb exactly, for every closed surface S in space. For any circle C in 3D and any smooth vector field F, one has F. dL = 0. There exists a smooth function f satisfying the identity Vf = (1 xy) ea, + (e + x2 ery) ay. The vector-valued integral as equals 0 for every closed surface S in space. By carefully selecting a smooth function F and closed surface S, one can arrange F) .dS = 48. REMEMBER: All your responses will be checked at the same time, and there is a limit of one submission per student (no second chances!)