Function Festival Fall 2000

Sarah Neely, Math Artist

Sarah f(x,y) Model 1

Sarah f(x,y) Model 2

Sarah f(x,y) winplot

My function is: Z = f(x,y) = ln(x^2+y^2+1)
and I am finding the directional derivatives,
grad Z.u, grad Z.v, from point A(3,3,3.56) to
points B(1,-2,1.79) and C(-3,3,2.94).

For AB = -2i-7j, the unit vector in the direction of AB is:
  u = -2i/(53^.5)-7j/(53^.5)

and AC = -6i-2j , the unit vector in the direction of AC is:
  v = 6i/(40^.5)- 2j/(40^.5)

Grad Z = (2x/(x^2+y^2+1))i+(2y/(x^2+y^2+1))j
      and then Grad Z at(3,3)=(6/35)i+(10/35)j

grad Z.u = [6/35)i+(10/35)j].[(-2/(53^.5))i-(7/(53^.5))j]
                = 0.2276260774

grad Z.v = [(6/35)i+(10/35)j].[(6/(40^.5))i+(-2/40^.5)j]
                = 5.443635115

Sarah f(x,y) Model 3

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