Math 251 Lecture 15: Friday, October 15th 1999.
Continuing with section 12.2, an example was given in which the limit
actually does exist along all paths. After trying a few paths, the
epsilon - delta method was used to prove that the limit exists.
We then moved on to section 12.3, and defined partial
derivatives. Properties of partial derivatives were
discussed, including Clairaut's Theorem, which states that
the mixed second-order partial derivatives of continuous
functions are equal.
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Revised 26 October 1999 by
John Hebron.