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Let f : R3 → R be de?ned by: f(x, y, z) = xy2+ x3z4+ y5z6
a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) .
b) Brie?y explain why f must be a di?erentiable function (you just need to "look" at the equations for the partial derivatives).
c) Find D~uf(2, 1, 1) where ~u is a unit vector in the direction of ~v = h4, 3,-1i .
d) Find an equation for the plane which is tangent to the surface de?ned by
xy2+ x3z4+ y5z6= 11
at the point (2, 1, 1) .
e) Use di?erentials to approximate the value of f(2.01, 1.02, 0.97) . Use a calculator to?nd a more accurate value, and compare.
Properties of Cross product If u, v and w are vectors and c is a number then u → * v → = -v → * w → (cu → ) * v → =
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Example of subtraction: Example: Subtract 78 from 136. Solution: 2 136 -78 ------ 58 While subtracting the units column, 6 - 8, a 10 that is b
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1. In Figure there are three cameras where the distance between the cameras is B, and all three cameras have the same focal length f. The disparity dL = x0 - xL, while the disparit
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