Information provided by the grader:
HW3:
Among the students who turned the assignment in, the mean, median, and max
were, respectively, 14.26, 15.875, and 19.75.
I apologize for how messy 3.1.5 probably is. I was going to make (b) and
(c) worth only 0.5 each, but then section 3.1 wasn't worth enough points
for how important it is. I recommend checking that I added correctly when
computing your total score, but don't double count the scores for this
first problem.
On 3.2.9, I took off a quarter point for using that a constant over
something diverging to infinite will go to 0. This fact doesn't seem to
have appeared in your book, so I don't think you can use it. I did allow
you to use things like 1/n -> 0, and even 1/\sqrt{n} -> 0, since we saw
these in 3.1.
On that same problem, I was going to take a half point off for moving a
limit under a square root, but then I realized that Theorem 3.2.10 allows
you to do this. Just be aware that since we haven't learned about
continuity yet, this sort of thing is not yet allowed for us with most
other continuous functions.
For 3.2.18, getting full credit required correct answers with good
justifications, which would probably use Theorem 3.2.11 (ratio test).
Note that 3.2.11 doesn't give us that L>1 implies divergence (although it
can easily be proven to be true). Since this is exercise 3.2.17 in the
book, I decided to give credit for it anyway.
HW6:
Also, only one student correctly proved that a continuous, periodic
function is bounded and uniformly continuous on the real numbers. One
common mistake was proving that the function was uniformly continuous and
bounded on every set in a cover for R (i.e., proving it locally), and
claiming, without referring to periodicity, that this proves it globally.
There were also at least a couple students who claimed that R is bounded.