A primary reinforcer

Determine if the vector field F→=-cosxcosy,sinxsiny,-sec2z{“version”:”1.1″,”math”:”F→=-cosxcosy,sinxsiny,-sec2z”} is conservative.  Be sure to fully support your conclusion.

Given the field F→=y+z,x,x{“version”:”1.1″,”math”:”F→=y+z,x,x”} is conservative, evaluate the work done from the point 0,0,0{“version”:”1.1″,”math”:”0,0,0″} to the point 3,10,7{“version”:”1.1″,”math”:”3,10,7″}

Set up an iterated double integral that expresses the area of the region bound by the parabola y=x2{“version”:”1.1″,”math”:”y=x2″} and the line y=4x+21{“version”:”1.1″,”math”:”y=4x+21″}.

Set up an iterated triple integral in the order dzdydx{“version”:”1.1″,”math”:”dzdydx”} for the volume of the region in the first octant enclosed by the cylinder x2+y2=9{“version”:”1.1″,”math”:”x2+y2=9″} and the plane z=6{“version”:”1.1″,”math”:”z=6″}.

Evaluate ∂w∂u{“version”:”1.1″,”math”:”∂w∂u”}at u,v=5,3{“version”:”1.1″,”math”:”u,v=5,3″} for the function wx,y,z=xz+yz-z2{“version”:”1.1″,”math”:”wx,y,z=xz+yz-z2″}where x=uv{“version”:”1.1″,”math”:”x=uv”}, y=uv{“version”:”1.1″,”math”:”y=uv”} and z=u{“version”:”1.1″,”math”:”z=u”}.

Find ∫π2πrt→dt{“version”:”1.1″,”math”:”∫π2πrt→dt”}, if it exists when rt→=2,5sint,12cost{“version”:”1.1″,”math”:”rt→=2,5sint,12cost”}

Consider r(t)→=2,5sint,12cost{“version”:”1.1″,”math”:”r(t)→=2,5sint,12cost”}. Find the unit tangent vector.

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