(a) Find the tangent plane to the surface with parametric equations
x=u v,y=3u^(2),z=u-v
at the point
(2,3,0)
. (b) Evaluate the line integral
\int_C xydx (x-y)dy
where
C
consists of line segments from
(0,0)
to
(2,0)
and from
(2,0)
to
(3,2)
. (c) Given that
F(x,y,z)=yzi xzj (xy 2z)k
is conservative, find the function
f
such that
F=gradf
. Hence or otherwise, evaluate the line integral
\int_C F*dr
, where
C
is the line segment from
(1,0,-2)
to
(4,6,3)
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