Comments:

2-42 = 30 pts (15 for each part)
2-43 = 30 pts (10 for each), graded as extra credit
2-44 = 30 pts
2-45 = 40 pts (20 for showing differentiability and 20 for showing the product
rule)
There was a maximum possible of 130 out of 100. The grade on the student's paper
is out of 100.

24 homeworks were handed in. Grades ranged from 30 to 120 with a mean of 91. On
average, however, students only received 70% of the possible points.

2-42 was good. A few showed differentiability and forgot to state what the value
of the gradient is, a minor deduction. Students should try to read the problems
a little more carefully.

2-43 was pretty good. I was impressed with people's solutions for showing
continuity at the origin. On part c, many students just assumed what was given
in the hint without actually showing it.

On 2-43 a, a couple students tried to take a limit as x tends to zero and as y
tends to zero separately, but we cannot do this because we are concerned with
the case where x and y tend to zero together.

On 2-43 b, most students properly calculated the limit and got 0/h2^2. Some
studends were concerned about the case h2=0, but this is wrong becasue as we
take the limit as y tends to zero, we assume that y is not zero, and thus h2 is
not zero.

As a side note, I would like to point out that I was very disappointed that
nobody used my method (the easiest method) to solve 2-43 a, which is by using
the fact that x^2*y is less than or equal to x^4+y^2. This is an implementation
of the arithmetic-geometric mean inequality. If students are not familiar with
this inequality, I would recommend that they familiarize themselves with it
becasue Dr. Jones is quite fond of it and it is helpful (or even necessary) to
solve many of his problems. Last year's Math 221 final had a problem where this
inequality had to be used.

On 2-44, I was generally very impressed by what I saw.

Some students had trouble with 2-45. The main problem was that students tried to
show the product rule without showing differentiabliity first, which is hard
because you can't implement 2-44 unless you are dealing with a differentiable
function. The best way to do this is to show differentiability first and then
to show the product rule.

Also, many students tried to solve it without the hint. One or two had some
degree of success, but if the author gives a hint, it is probably a good idea
to use that hint.

In general, a few students seem to think that every single math problem in the
world is best solved with epsilons and deltas. These proofs tend to be
confusing and on many of these problems they do not end up really proving
anything. Usually the stuff being discussed in the book is the stuff students
will need to solve the problems.