Date Due
|
Page
|
Problems
|
Comments
|
| 19 Jan |
27 |
# 6, 10, 14, 20, 29, 31 |
|
| 26 Jan |
29
54 |
# 41
# 2, 4, 5, 6(d), 10 |
|
| 2 Feb |
55 |
# 14, 15, 17, 21 |
|
| 9 Feb |
55 |
# 16, 18, 19, 26, 34, 36, 40 |
|
| 16 Feb |
Exam 1 |
Chapters 0 and 1 |
|
| 24 Feb |
79 |
# 2, 4, 5, 7, 9 |
Note the Friday due date. Please turn in your solutions to my mailbox or to my office by 5pm.
HW 5 Solutions
|
| 1 Mar |
79 |
# 10, 17, 19, 22, 23 |
|
| 15 Mar |
104 |
# 2, 5, 7, 8, 9, 11 |
When proving continuity you almost always have to start with
\( |f(x)-f(a)| \) and work to factor out \( |x-a| \).
Usually there will be something else besides the \( |x-a| \);
this has to be bounded. There are lots of algebraic techniques
that can help with this. These exercises ask you to use some
of them. Once you have \( |f(x)-f(a)| < M|x-a| < M\delta \) you
know how to choose the \( \epsilon \) and can now give the proof.
HW 7 Solutions (Corrected)
|
| 22 Mar |
104 |
# 13, 15, 16, 18, 27, 34 |
In #15, there are several ways to approach this problem.
See my comments on the discussion group on Blackboard for
more comments about this problem.
In #16, note that the second sentence should end with
\( x^x = e^{x\ln x} \).
Each of the first four exercises has some connection with
an exercise in an earlier homework assignment. You might
want to refresh your memory about the earlier problem
before you solve these problems.
The last two exercises have to do with open, closed, and compact sets.
HW 8 Solutions
|
| 22 Mar |
Exam 2 |
Sections 2.1--3 and 3.1--3 |
|
| 5 Apr |
105 |
# 19, 20, 22 |
Note that in #19 (for \( fg \)) and for #20 you do not have to prove,
only justify.
When proving uniform continuity you almost always have to start with
\( |f(x)-f(y)| \) and work to factor out \( |x-y| \).
Usually there will be something else besides the \( |x-y| \);
this has to be bounded. Usually, it's not difficult to find the
needed bound, but you do have to explain how the bound was obtained.
Once you have \( |f(x)-f(y)| < M|x-y| < M\delta \) you
know how to choose the \( \epsilon \) and can now give the proof.
(Doesn't this sound familiar?)
HW 9 Solutions
|
| 12 Apr |
106 |
# 41, 42, 43 |
These problems should be fairly straightforward.
They form a nice transition as we move into the final
part of the course: differentiation.
The differentiation results should all be familiar,
but now you will know exactly why they are true.
HW 10 Solutions
|
| 19 Apr |
129 |
# 5, 11, 20, 21, 33 |
These problems should be fairly straightforward.
They form a nice conclusion to the course.
There is not a single \( \epsilon \) or \( \delta \)
in any of these solutions.
When you use the Mean Value Theorem or l'Hopital's Rule,
be sure you show that you have addressed all of the hypotheses.
You can use known differentiation formulas, when they apply.
For #11, be sure you show that all hypotheses of the Chain Rule
are satisfied.
HW 11 Solutions
|
30 Apr
9:00 am |
Final Exam |
Chapters 1-4 |
|