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(Solved): (a) Find the tangent plane to the surface with parametric equations x=u v,y=3u^(2),z=u-v at the poin ...



(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)

[8, 8, 9]



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