Richard
Skinner

rls2723

Sheet #25

Week #4

Problem
4.3.1


http://208.166.239.244/3_4_1.htm

The function
f:R^{3}>R^{2} is defined by:
.
Let
.
(a) Find the
matrix (J_{xo}f or df/dx) representing the differential of this
function, d_{xo}f.
Solution:
.
d_{xo}f 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(x_{0}) + d_{xo}f