IMPORTANT: You only get one try at this entire multi-response problem. Put a response in every box before choosing “Subm

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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 “0“ for False. equation editor If is a
vector field, then is a vector field. equation editor If is a
vector field, then is a vector field. equation editor If is a
smooth scalar field, then . equation editor For any circle in 3D
and any smooth function , one has equation editor Given any region
of 3D space and any vector field satisfying in that region, there
must exist some scalar-valued function satisfying the identity
throughout the given region. equation editor Whenever and are
vector fields satisfying at all points in space, the difference is
a constant vector. equation editor . equation editor . equation
editor For any constant vector field and spherical shell , one has
equation editor There exists a vector field satisfying equation
editor The magnetic flux equals 0 Wb exactly, for every closed
surface in space. equation editor For any circle in 3D and any
smooth vector field , one has equation editor There exists a smooth
function satisfying the identity equation editor The vector-valued
integral equals for every closed surface in space. equation editor
By carefully selecting a smooth function and closed surface , one
can arrange . REMEMBER: All your responses will be checked at the
same time, and there is a limit of one submission per student (no
second chances!). FILL IN THE BOXES NOT ALREADY FILLED IN.
THANKS

Important You Only Get One Try At This Entire Multi Response Problem Put A Response In Every Box Before Choosing Subm 1 (108.74 KiB) Viewed 32 times

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. 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 f) = 0. For any circle C in 3D and any smooth function f, one has fy Vf.dL = 0. Given any region of 3D space and any vector field F satisfying 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 G are vector fields satisfying div F = div G at all points in space, the difference G-F is a constant vector. T curl(F+G) = curl(F) + curlG) curl(FG) = curl(F) curl. For any constant vector field F and spherical shell S, one has SI F. ds = 0. Sle ! There exists a vector field F satisfying V F = (x, y, z). The magnetic flux Ⓡ = BdS 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 fit F. dL = 0. There exists smooth function f satisfying the identity Vf=(1 zy)e+ya, + (ell + z?e?)ay. The vector-valued integral dS equals 0 for every closed surface S in space. M By carefully selecting a smooth function F and closed surface S, one can arrange Mla (VxF) ds = 47. REMEMBER: All your responses will be checked at the same time, and there is a limit of one submission per student (no second chances!).