## Daily Homework

Generally, Daily Homework will be assigned every class session and will be due by the beginning of the next class session. The majority of the Daily Homework assignments are to be completed via WeBWorK, which is an online homework system. Once on the main WeBWorK page, click on DErnst_136 to access the WeBWorK homework for our class. You should log in with your NAU credentials. In addition to the problems done online, you will also be asked to occasionally submit written work. With some exceptions, each exercise (WeBWork or written) from the Daily Homework will be worth a point. Unless a student has a documented excused absence, late Daily Homework will not be accepted. However, if necessary, the scores will be “curved.”

**Daily Homework 1:**Complete #1-16 from Are You Ready for Calculus?**Note:**This assignment is worth 10 points. (Due Wednesday, August 29)**Daily Homework 2:**Complete #19ab, 20a, 22a, 25-30, 32-34 from Are You Ready for Calculus?**Note:**This assignment is worth 10 points. (Due Thursday, August 30)**Daily Homework 3:**Read Chapter 1 of the course packet. Also, complete the corresponding problems on WeBWorK. (Due Wednesday, September 5 by~~3:30PM~~10:00PM)**Daily Homework 4:**Re-read Chapter 1 of the course packet. Also, complete the corresponding problems on WeBWorK. I made a short video that should help you with the first few problems. You can find the video here. (Due Thursday, September 6 by 3:30PM)**Daily Homework 5:**Read Sections 2.1 and 2.2 and complete the corresponding problems on WeBWorK. (Due Friday, September 6 by 6:00PM)**Daily Homework 6:**Read Section 2.3 and complete the corresponding problems on WeBWorK. (Due Monday, September 10 by 3:30PM)**Daily Homework 7:**Read Section 2.4 and complete the corresponding problems on WeBWorK. (Due Wednesday, September 12 by 8:00PM)**Daily Homework 8:**Re-read Section 2.4 and complete the corresponding problems on WeBWorK. (Due Thursday, September 13 by 3:30PM)**Daily Homework 9:**Read Section 2.6 and complete the corresponding problems on WeBWorK. (Due Friday, September 14 by 3:30PM)**Daily Homework 10:**Read Section 2.5 and complete the corresponding problems on WeBWorK. (Due Monday, September 17 by 3:30PM)**Daily Homework 11:**Read Section 2.7, complete the corresponding problems on WeBWorK, and in addition, compute the derivative of each of the following functions using the limit definition of the derivative (all work must be shown). (Due Wednesday, September 19 by 3:30PM)- $f(x)=3x^2-x$
- $g(x)=\sqrt{1-x}$

**Daily Homework 12:**Read Section 2.8 and complete the corresponding problems on WeBWorK. (Due Thursday, September 20 by 3:30PM)**Daily Homework 13:**Read Sections 3.1 and 3.2 and complete the corresponding problems on WeBWorK. (Due Wednesday, September 26 by 3:30PM)**Daily Homework 14:**Read Section 3.4 and complete the corresponding problems on WeBWorK. (Due Thursday, September 27 by 3:30PM)**Daily Homework 15:**Read Section 3.3 and complete the corresponding problems on WeBWorK. (Due Friday, September 28 by 3:30PM)**Daily Homework 16:**Read Sections 3.5 and Sections 3.6 and complete the corresponding problems on WeBWorK. (Due Monday, October 1 by 3:30PM)**Daily Homework 17:**Read Section 3.7 and complete the corresponding problems on WeBWorK. (Due Thursday, October 4 by 3:30PM)**Daily Homework 18:**Read Section 3.8 and complete the corresponding problems on WeBWorK. (Due Friday, October 5 by 3:30PM)**Daily Homework 19:**Read Section 4.5 and complete the corresponding problems on WeBWorK. (Due Monday, October 8 by 3:30PM)**Daily Homework 20:**Read Section 3.10 and complete the corresponding problems on WeBWorK. (Due Wednesday, October 10 by 3:30PM)**Daily Homework 21:**Read Section 3.11 and complete the corresponding problems on WeBWorK. (Due Thursday, October 11 by 3:30PM)**Daily Homework 22:**Read Section 4.1 and complete the corresponding problems on WeBWorK. (Due Wednesday, October 17 by 9:00PM)**Daily Homework 23:**Read Sections 2.9, 2.10, 2.11, and 4.2 and complete the corresponding problems on WeBWorK. (Due Thursday, October 18 by 3:30PM)**Daily Homework 24:**Re-read Section 4.2 and then complete the following exercises. (Due Friday, October 19 in class)- Sketch a graph of the function with the following properties:
- $f(-4)=2$, $f(-2)=5$, $f(-1)=2$, and $f(0)=0$
- vertical asymptote at $x=3$ such that $\displaystyle \lim_{x \to 3^{-}}f(x)=-\infty$ and $\displaystyle \lim_{x \to 3^{+}}f(x)=\infty$
- horizontal asymptote at $y=0$ such that $\displaystyle \lim_{x \to \infty}f(x)=0$ and $\displaystyle \lim_{x \to -\infty}f(x)=0$
- $f'(-2)=0$ and $f'(0)=0$
- $f'(x) >0$ on $(-\infty,-2)$
- $f'(x)< 0$ on $(-2,0)$, $(0,3)$, and $(3,\infty)$
- $f^{\prime\prime}(-4)=0$, $f”(-1)=0$, and $f”(0)=0$
- $f^{\prime\prime}(x) >0$ on $(-\infty, -4)$, $(-1,0)$, and $(3,\infty)$
- $f^{\prime\prime}(x) <0$ on $(-4,-1)$ and $(0,3)$

- Sketch the graph of the following functions by following the algorithm we discussed in class.
- $f(x) = \displaystyle \frac{x^2}{x-2}$
- $g(x) = \displaystyle xe^x$

- Sketch a graph of the function with the following properties:
**Daily Homework 25:**Read Section 4.4 and then complete the following exercises. (Due Monday, October 22 in class)- Sketch the graph of a function that is continuous on $[0,4]$, has an absolute min at 1, an absolute max at 2 and a local min at 3.
- Sketch the graph of a function on $[1,4]$ that has an absolute max but no absolute min.
- Sketch the graph of a function on $[1,4]$ that is
*not*continuous but has both an absolute max and an absolute min. - Find the absolute max and absolute min values of $f$ on the given interval. You may assume the function is continuous on the interval.
- $f(x)=3x^4-4x^3-12x^2+1$, $[-2,3]$
- $f(x)=x-\ln x$, $[0.5,2]$ (You may use a calculator to evaluate $x$-values after you have the critical numbers.)
- $f(x)=x-2\arctan x$, $[0,4]$

**Daily Homework 26:**Re-read Section 4.4 and complete the corresponding problems on WeBWorK. (Due Wednesday, October 24 by 3:30PM)**Daily Homework 27:**Read Section 4.4 and complete the corresponding problems on WeBWorK. (Due Friday, October 26 by 3:30PM)**Daily Homework 28:**Read Section 4.8 and complete the corresponding problems on WeBWorK. In addition, complete the following exercises, which are due at the beginning of class. (Due Monday, October 29 by 3:30PM for WeBWorK)- On a toll road a driver takes a time stamped toll-card from the starting

booth and drives directly to the end of the toll section. After

paying the required toll, the driver is surprised to receive a

speeding ticket along with the toll receipt. Which of the

following best describes the situation? (a) The booth attendant does not have enough information to prove that the driver was speeding. (b) The booth attendant can prove that the driver was speeding

during his trip. (c) The driver will get a ticket for a lower speed than his actual maximum speed. (d) Both (b) and (c). **True**or**False**? For $f(x) = |x|$ on the interval $[-\frac{1}{2}, 2]$, you can find a

point $c$ in $(-\frac{1}{2},2)$ such that

\[f'(c) = \frac{f(2) – f(-\frac{1}{2})}{2-(-\frac{1}{2})}.\]- Two runners start a race at the same time and finish in a tie. Prove that at some moment during the race they had the same velocity. (
*Hint:*Let $p_1(t)$ and $p_2(t)$ be position functions of runners 1 and 2, respectively, and consider the function $f(t)=p_1(t)-p_2(t)$.) **Daily Homework 29:**Read Section 4.3 and complete the corresponding problems on WeBWorK. (Due Wednesday, October 31 by 3:30PM)**Daily Homework 30:**Read Section 5.1 and complete the corresponding problems on WeBWorK. (Due Wednesday, November 7 by 3:30PM)**Daily Homework 31:**This assignment is optional. If you complete it, I will add 3 points to your homework total. Answer the following three questions. (Due Thursday, November 8)- What can you do differently to improve?
- What should you continue to do?
- What can Dana do better?

**Daily Homework 32:**Read Section 5.2 and complete the corresponding problems on WeBWorK. (Due Friday, November 9 by 8PM)**Daily Homework 33:**Re-read Section 5.2 and complete the following problems. (Due Friday, November 16 in class)- Consider the integral $\displaystyle \int_0^1 3x+1\ dx$.
- Compute the value of the integral using a limit of Riemann sums and right endpoints.
- Verify that your answer is correct by interpreting the integral in terms of areas of geometric shapes.

- Compute the value of $\displaystyle \int_0^1 x^2-4x\ dx$ using a limit of Riemann sums and right endpoints.

- Consider the integral $\displaystyle \int_0^1 3x+1\ dx$.
**Daily Homework 34:**Read Section 5.5 and complete the corresponding problems on WeBWorK. (Due Monday, November 19 by 8PM)**Daily Homework 35:**Read Section 5.3 and complete the corresponding problems on WeBWorK. (Due Wednesday, November 21 by 8PM)**Daily Homework 36:**Read Section 5.4 and complete the corresponding problems on WeBWorK. (Due Tuesday, November 27 by 8PM)**Daily Homework 37:**Read Section 5.6 and complete the corresponding problems on WeBWorK. (Due Wednesday, November 28 by 8PM)**Daily Homework 38:**Read Section 5.6 and complete the corresponding problems on WeBWorK. (Due Thursday, November 29 by 8PM)**Daily Homework 39:**Read Section 6.1 and complete the corresponding problems on WeBWorK. (Due Wednesday, December 5 by 8PM)

## Weekly Homework

The Weekly Homework will be graded for more than the correct answer. In particular, intermediate steps will be graded, as well as your ability to present a complete solution. Moreover, your write-ups should be neatly written and make proper use of mathematical notation. The problems for your Weekly Homework will cover a subset of material covered the previous week. This will provide you with an opportunity to reflect on previous material and to deepen your understanding. Sometimes the problems will be identical to problems that you have already done and sometimes they will be new. Typically, the Weekly Homework assignments will be due on Wednesdays. Each Weekly Homework assignment will be worth 10 points, regardless of the number of problems. You are allowed to submit up to two late Weekly Homework assignments with no penalty. Also, two of your lowest Weekly Homework scores will be dropped.

**Weekly Homework 1:**For this assignment, you have to complete 3 relatively simple tasks. (Due Friday, August 31)- Stop by my office (Room 119 in Adel Mathematics) and say hello. If I’m not there, slide a note under the door telling me you stopped by.
- Send me an email at dana.ernst@nau.edu and tell me 3 important things that are in the syllabus.
*Note:*Listing all of the exams dates only counts as one item. If you are the first person to point out a typo, I will give you a*bonus point*for each typo found. - Provide a brief introduction (2-3 sentences) about yourself in the appropriate forum in Bb Learn. It should be obvious which forum to use. Instead of replying to someone else’s introduction, each person should start a new thread. However, you are welcome to reply to each other’s introductions.

**Weekly Homework 2:**Complete exercises 1.4.9 (only part 3), 1.4.16, 1.4.23 (explain answer), 1.4.27, 1.4.28 (just the first column) from course packet. I expect your solutions to be organized, complete, and neatly written. (Due Friday, September 7)**Weekly Homework 3:**Complete exercises found here (PDF). (Due Wednesday, September 12)**Weekly Homework 4:**Complete exercises found here (PDF). (Due Wednesday, September 19)**Weekly Homework 5:**Complete exercises found here (PDF). (Due Wednesday, October 3)**Weekly Homework 6:**Complete exercises found here (PDF). (Due Friday, October 12)**Weekly Homework 7:**Complete exercises found here (PDF). (Due Thursday, October 25)**Weekly Homework 8:**Complete exercises found here (PDF). (Due Friday, November 2)**Weekly Homework 9:**Complete exercises found here (PDF). (Due Thursday, November 15)**Weekly Homework 10:**Complete exercises found here (PDF). (Due Friday, November 30)