**Unformatted text preview: **lative to the coordinate
system whose origin is at (2, 1, −1) then you get the slightly simpler equation of a
plane through the this new origin 4d − 5dy − dz = 0.
(b) If the point Q(2.1, 0.9, k ) lies near P (2, 1, −1) and on the surface, use linear approximation to approximate the value of k .
Answer:
On the tangent plane we have 4(.1) − 5(−.1) − dz = 0 hence .9 = dz = z + 1 or
z = −.1. Hence the z coordinate of the corresponding point on the surface will be
z = −.1 + error and we are assuming that the changes are small enough so that the
error term is negligible and our linear approximation is fairly accurate.
Another approach is to assume that z = z (x, y ) is a function of x and y...

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