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Richard
Skinner
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rls2723
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Sheet #25
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Week #4
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Problem
4.3.1
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http://208.166.239.244/3_4_1.htm
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The function
f:R3->R2 is defined by:
.
Let
.
(a) Find the
matrix (Jxof or df/dx) representing the differential of this
function, dxof.
Solution:
.
dxof is this matrix evaluated at .
This comes
out to be
.
(b) Use the
result of (a) to find an approximate value for 
.
Solution:
The best affine
approximation to a function is given by the sum of the value of the function
at a given location and its displacement along its tangent line. This is
shown in the following equation:
f(x) »
f(x0) + dxof
