Show that the force field F= (y2-2xyz3)i+( 3+2xy-x2z3)j+(6z3-3x2yz2)k is a conservative forcefield.
Hence determine the potential F and the work done in moving a particle from (3,0,-2) to (-2,1,0) in
the force field . (For conservative forcefield curlF=0 ) (6mks)
i) Determine directional derivative of at P(-1, 0, 3) from P in the
direction of Q(2,1,-2). (4mks)
ii) A function f(x,y)=x2-y2+3xy.. Find the rate of change of f(x,y) from P(1,0) to
Q(-1,-2). What is the maximum rate of change of f(x,y)? (4mks)
iii) Find the equation of the tangent plane to z=x2+y2 +2xy at the point (1,-1,2). (4mks)

. If find given that and at t=0.
(4mks)

. Evaluate and C the curve given by C:
x=t ,y=t2+1, t=0 to t=1. (4mks)

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