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TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. (4 marks) 1) Let f(x,y,z) be a function. The line integral of curl(Vf)) around any circle is zero. 2) The flux of the curl of a vector field through the disc x2 + y2<. 1, z = 0 is always zero. 3) If a function f(x,y) has a critical point at (0,0) then div(grad (f)) (0,0) is zero. 4) The gradient of the divergence of the curl of a vector field is constantly zero. 5) The points in the 3d space that satisfy 0 = π/4 and p = 7/4 in spherical coordinates form a surface which is part of a cone. 1) 2) 3) 4) 5)
Please briefly explain your answer, thank you.
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