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Calc III midterm 3 Question and answers 100% correct 2025

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Calc III midterm 3 Question and answers 100% correct 2025 curl equation - correct answers (F3y-F2z, F1z-F3x, F2x, F1y) polar coordinates - correct answers x=rcos(theta), y=rsin(theta) dA=rdrdtheta cylindrical coordinates - correct answers x=rcos(theta), y=rsin(theta), z=z, dV=rdrdthetadz x^2+y^2<R^2 - correct answers polar 0<r<R x>0 - correct answers polar -.5pi<theta<.5pi x^2+y^2+z^2<R^2 - correct answers spherical 0<ro<R z>0 - correct answers spherical 0<phi<.5pi sqrt(x^2+y^2)<z - correct answers spherical .25pi<phi<.5pi what makes a vector field incompressible - correct answers divergence everywhere is 0 What makes a vector field irrotational - correct answers curl everywhere is 0 What does it mean if a vector field is conservative - correct answers there is a function such that F=t

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Calc III
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Calc III

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Uploaded on
April 17, 2025
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Written in
2024/2025
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Calc III midterm 3 Question and answers
100% correct 2025
curl equation - correct answers (F3y-F2z, F1z-F3x, F2x, F1y)


polar coordinates - correct answers x=rcos(theta), y=rsin(theta) dA=rdrdtheta


cylindrical coordinates - correct answers x=rcos(theta), y=rsin(theta), z=z,
dV=rdrdthetadz


x^2+y^2<R^2 - correct answers polar 0<r<R


x>0 - correct answers polar -.5pi<theta<.5pi


x^2+y^2+z^2<R^2 - correct answers spherical 0<ro<R


z>0 - correct answers spherical 0<phi<.5pi


sqrt(x^2+y^2)<z - correct answers spherical .25pi<phi<.5pi


what makes a vector field incompressible - correct answers divergence
everywhere is 0


What makes a vector field irrotational - correct answers curl everywhere is 0


What does it mean if a vector field is conservative - correct answers there is a
function such that F=trianglef
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