## Calculus I

## Preview Assignments

For most class meetings this semester, you will be given a graded Preview Assignment, which is intended to be an assignment that previews our work in the upcoming class period with some questions for you to answer and some reading for you to complete. You should normally be able to complete one of these assignments in under an hour. The default grade on these assignments is 4/4. Point deductions follow from lack of completion or if it appears that the assignment was not taken seriously. In the event that no assignment is submitted, the grade is zero. For more details, see the syllabus.

**Preview Homework 1:**Skim Section 1.1 and complete Preview Activity 1.1 from Active Calculus. (Due Thursday, January 24)**Preview Homework 2:**Skim Section 1.2 and complete Preview Activity 1.2 from Active Calculus. (Due Monday, January 28)**Preview Homework 3:**Skim Section 1.3 and complete Preview Activity 1.3 (page 21) from Active Calculus. (Due Monday, February 4)**Preview Homework 4:**Skim Section 1.4 and complete Preview Activity 1.4 (page 31) from Active Calculus. (Due Wednesday, February 6)**Preview Homework 5:**Skim Section 2.3 and complete Preview Activity 2.3(a)(b)(c) on pages 94-95 from Active Calculus. (Due Thursday, February 14)**Preview Homework 6:**Skim Section 2.6 and complete Preview Activity 2.6 on pages 120-121 from Active Calculus. (Due Monday, February 25)**Preview Homework 7:**Skim Section 2.8 and complete Preview Activity 2.8 on pages 139-140 from Active Calculus. (Due Wednesday, March 6)**Preview Homework 8:**Skim Section 3.1 and complete Preview Activity 3.1 on pages 152-153 from Active Calculus. (Due Thursday, March 7)**Preview Homework 9:**Skim Section 4.1 and complete Preview Activity 4.1 on pages 196-197 from Active Calculus. (Due Thursday, April 4)**Preview Homework 10:**Skim Section 4.2 and complete Preview Activity 4.2 on pages 209-210 from Active Calculus. (Due Monday, April 8)

## Daily Homework

Daily Homework will be assigned most class meetings and will typically be due the day 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 #1-10, 14 from Are You Ready for Calculus? (PDF)**Note:**This assignment is worth 10 points. (Due Wednesday, January 16)**Daily Homework 2:**Complete #11-13, 15(b), 19(a)(b), 20(a), 22(a), 25-30 from Are You Ready for Calculus? (PDF)**Note:**This assignment is worth 10 points. (Due Thursday, January 17)**Daily Homework 3:**Complete the corresponding problems on WeBWorK. (Due Friday, January 18 by 8PM) I made a short video last semester that illustrates how to get started with WeBWorK. You can find the video here (YouTube).**Note:**There are some inconsistencies in this video due to the fact that I made it for last semester’s class, but it should still be useful.**Daily Homework 4:**Complete the corresponding problems on WeBWorK. (Due Wednesday, January 23 by 9PM)**Daily Homework 5:**Complete the corresponding problems on WeBWorK. (Due Thursday, January 24 by 9PM)**Daily Homework 6:**Complete the corresponding problems on WeBWorK. (Due Friday, January 25 by 9PM)**Daily Homework 7:**Complete the corresponding problems on WeBWorK. (Due Monday, January 28 by 9PM)**Daily Homework 8:**Complete the corresponding problems on WeBWorK.**Note:**For problem 2, reviewing Example 1.2(b) from Section 1.2 of Active Calculus would be helpful. (Due Wednesday, January 30 by 9PM)**Daily Homework 9:**Complete the corresponding problems on WeBWorK. (Due Thursday, January 31 by 9PM)**Daily Homework 10:**Complete the corresponding problems on WeBWorK. (Due Friday, February 1 by 9PM)**Daily Homework 11:**Complete the corresponding problems on WeBWorK. (Due Monday, February 4 by 9PM)**Daily Homework 12:**Complete the corresponding problems on WeBWorK. (Due Wednesday, February 6 by 9PM)**Daily Homework 13:**Complete the corresponding problems on WeBWorK. (Due Thursday, February 7 by 9PM)**Daily Homework 14:**Complete the corresponding problems on WeBWorK. (Due Wednesday, February 13 by 9PM)**Daily Homework 15:**Complete the corresponding problems on WeBWorK. (Due Thursday, February 14 by 9PM)**Daily Homework 16:**Complete the corresponding problems on WeBWorK. (Due Friday, February 15 by 9PM)**Daily Homework 17:**Complete the corresponding problems on WeBWorK. (Due Monday, February 18 by 9PM)**Daily Homework 18:**Complete the corresponding problems on WeBWorK. (Due Thursday, February 21 by 9PM)**Daily Homework 19:**Complete the corresponding problems on WeBWorK. (Due Friday, February 22 by 9PM)**Daily Homework 20:**Complete the corresponding problems on WeBWorK. (Due Monday, February 25 by 9PM)**Daily Homework 21:**Complete the corresponding problems on WeBWorK. (Due Wednesday, February 27 by 9PM)**Daily Homework 22:**Complete the corresponding problems on WeBWorK. (Due Thursday, February 28 by 9PM)**Daily Homework 23:**Complete the corresponding problems on WeBWorK. (Due Wednesday, March 6 by 9PM)**Daily Homework 24:**Complete the corresponding problems on WeBWorK. (Due Thursday, March 7 by 9PM)**Daily Homework 25:**Complete the corresponding problems on WeBWorK. (Due Friday, March 8 by 9PM)**Daily Homework 26:**Complete the corresponding problems on WeBWorK. (Due Monday, March 11 by 9PM)**Daily Homework 27:**Complete the corresponding problem on WeBWorK. In addition, complete the following exercises. (Due Wednesday, March 13 in class for written work, 9PM for WeBWorK)**Note:**Due to my absence on my Monday, you may turn in the written problems on Thursday at the beginning of 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 28:**Complete the corresponding problems on WeBWorK. (Due Thursday, March 14 by 9PM)**Daily Homework 29:**Complete the corresponding problems on WeBWorK. (Due Friday, March 15 by 9PM)**Daily Homework 30:**Complete the following exercises. (Due Monday, March 25 in class for written work)- 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 31:**Complete the corresponding problems on WeBWorK. (Due Wednesday, March 27 by 9PM)**Daily Homework 32:**Complete the corresponding problems on WeBWorK. (Due Thursday, March 28 by 9PM)**Daily Homework 33:**Complete the corresponding problems on WeBWorK. In addition, complete the following exercises. (Due Thursday, April 4 in class for written work, 9PM 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 $f(t)=p_1(t)-p_2(t)$.)

- 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
**Daily Homework 34:**Complete the following exercises. (Due Monday, April 8 in class)- Do Exercise 2 on page 206 of Active Calculus (PDF).
- Do Exercise 4 on page 207 of Active Calculus (PDF).

**Daily Homework 35:**Complete the following exercises. (Due Wednesday, April 10 in class)- Do Exercise 3 on page 206 of Active Calculus (PDF).
- Let $v(t)=−9.8t+49$ be velocity function for some object, where $t$ is measured in seconds and $v(t)$ is measured in meters.
- Sketch the graph of $v$ on the interval $[0,10]$. Your graph should include labels for $x$-intercept(s) and $y$-intercept (if either exist).
- Find the net distance travelled by the object over the interval $[0,10]$ using areas of geometric shapes.
- Find the total distance travelled by the object over the interval $[0,10]$ using areas of geometric shapes.

**Daily Homework 36:**Complete the corresponding problems on WeBWorK. (Due Thursday, April 11 by 9PM)**Daily Homework 37:**Complete the corresponding problems on WeBWorK. (Due Friday, April 12 by 9PM)**Daily Homework 38:**Complete the corresponding problems on WeBWorK. (Due Monday, April 15 by 9PM)**Daily Homework 39:**Complete the corresponding problems on WeBWorK. (Due Wednesday, April 17 by 9PM)**Daily Homework 40:**Complete the corresponding problems on WeBWorK. (Due Thursday, April 18 by 9PM)**Daily Homework 41:**Complete the corresponding problems on WeBWorK. (Due Friday, April 19 by 9PM)**Daily Homework 42:**Complete the corresponding problems on WeBWorK. (Due Monday, April 22 by 9PM)**Daily Homework 43:**Complete the corresponding problems on WeBWorK. (Due Wednesday, April 24 by 9PM)**Daily Homework 44:**Complete the corresponding problems on WeBWorK. (Due Wednesday, May 1 by 9PM)

## 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. 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 2 relatively simple tasks. (Due by 5PM on Friday, January 18)- 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:*As an example, listing all of the exams dates only counts as one item. Also, if you are the first person to point out a typo in the syllabus, I will give you a*bonus point*for each typo found. The bonus points will be added to your homework total. This is likely the only opportunity that will arise for you to get bonus points.

**Weekly Homework 2:**Complete exercises found here (PDF). (Due Friday, January 25)**Weekly Homework 3:**Complete exercises found here (PDF). (Due Friday, February 1)**Weekly Homework 4:**Complete exercises found here (PDF). (Due Friday, February 8)- There is no Weekly Homework assignment due the week of Friday, February 15. Instead, you should submit a portfolio that contains the work that you’ve done for the in-class activities, as well as your work for the Daily Homework. Your portfolio is due by Friday, February 15. When you submit your portfolio, please include a table of contents that indicates where various items can be found. For more information, check out the Portfolio Expectations (PDF)
**Weekly Homework 5:**Complete exercises found here (PDF). (Due Friday, February 22)**Weekly Homework 6:**Complete exercises found here (PDF). (Due Friday, March 1)**Weekly Homework 7:**Complete exercises found here (PDF). (Due Friday, March 15)**Weekly Homework 8:**Complete exercises found here (PDF). (Due Friday, March 29)**Weekly Homework 9:**Complete exercises found here (PDF). (Due Friday, April 12)**Weekly Homework 10:**Complete exercises found here (PDF). (Due Friday, April 19)**Weekly Homework 11:**Complete exercises found here (PDF). (Due Friday, April 26)