## 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. 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:**Read the syllabus and write down 5 important items.*Note:*All of the test dates only count as one item. Turn in on your own paper at the beginning of class. This assignment is worth 5 points. (Due Wednesday, January 15)**Daily Homework 2:**Accept the invitation to the class Google Group. I will be sending out invitations via email during the first couple days of classes. If you’d prefer to use an email address other than your NAU address, please let me know. This assignment is worth 5 points. (Due Friday, January 17)**Daily Homework 3:**Stop by my office (Adel 119) and say hello. If I’m not there, slide a note under my door indicating that you stopped by (please put your first and last name on your note). This assignment is worth 5 points. (Due Friday, January 24)**Daily Homework 4:**Complete the corresponding problems on WeBWorK. I made a short video 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 my Fall 2012 class, but it should still be useful. (Due Wednesday, January 15 by 11PM)**Daily Homework 5:**Complete the corresponding problems on WeBWorK. (Due Thursday, January 16 by 11PM)**Daily Homework 6:**Complete the corresponding problems on WeBWorK. (Due Friday, January 17 by 11PM)**Daily Homework 7:**Complete the corresponding problems on WeBWorK. (Due Wednesday, January 22 by 11PM)**Daily Homework 8:**Read Sections 2.1 and 2.2 and complete the corresponding problems on WeBWorK. (Due Thursday, January 23 by 11PM)**Daily Homework 9:**Read Section 2.3 and complete the corresponding problems on WeBWorK. (Due Monday, January 27 by 11PM)**Daily Homework 10:**Read Section 2.4 and complete the corresponding problems on WeBWorK. (Due Wednesday, January 29 by 11PM)**Daily Homework 11:**Re-read Section 2.4 and complete the corresponding problems on WeBWorK. (Due Friday, January 31 by 11PM)**Daily Homework 12:**Read Section 2.6 and complete the corresponding problems on WeBWorK. (Due Monday, February 3 by 11PM)**Daily Homework 13:**Read Section 2.7 and complete the corresponding problems on WeBWorK (Due Wednesday, February 5 by 11PM). In addition, compute the derivative of each of the following functions using the limit definition of the derivative (all work must be shown and these are due in class).- $f(x)=3x^2-x$
- $g(x)=\sqrt{1-x}$

**Daily Homework 14:**Read Section 2.5 and complete the corresponding problems on WeBWorK. (Due Thursday, February 6 by 11PM)**Daily Homework 15:**Read Sections 3.1 and 3.2 and complete the corresponding problems on WeBWorK. (Due Wednesday, February 12 by 11PM)**Daily Homework 16:**Read Section 3.3 and complete the corresponding problems on WeBWorK. (Due Thursday, February 13 by 11PM)**Daily Homework 17:**Read Section 3.4 and complete the corresponding problems on WeBWorK. (Due Friday, February 14 by 11PM)**Daily Homework 18:**Read Section 2.8 and complete the corresponding problems on WeBWorK. (Due Monday, February 17 by 11PM)**Daily Homework 19:**Read Section 3.5 and complete the corresponding problems on WeBWorK. (Due Wednesday, February 19 by 11PM)**Daily Homework 20:**Read Section 3.6 and complete the corresponding problems on WeBWorK. (Due Friday, February 21 by 11PM)**Daily Homework 21:**Read Section 3.7 and complete the corresponding problems on WeBWorK. (Due Monday, February 24 by 11PM)**Daily Homework 22:**Read Section 3.8 and complete the corresponding problems on WeBWorK. (Due Wednesday, February 26 by 11PM)**Daily Homework 23:**Read Section 3.10 and complete the corresponding problems on WeBWorK. (Due Thursday, February 27 by 11PM)**Daily Homework 24:**Read Section 3.11 and complete the corresponding problems on WeBWorK. (Due Wednesday, March 5 by 11PM)**Daily Homework 25:**Read Section 4.1 and complete the corresponding problems on WeBWorK. (Due Friday, March 7 by 11PM)**Daily Homework 26:**Read Sections 2.9-2.11 and complete the corresponding problems on WeBWorK. (Due Monday, March 10 by 11PM)**Daily Homework 27:**Read Section 4.2 and complete the corresponding problems on WeBWorK. (Due Wednesday, March 12 by 11PM)**Daily Homework 28:**Complete the following exercises. (Due Friday, March 14 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 $(3,\infty)$
- $f^{\prime\prime}(-4)=0$, $f^{\prime\prime}(-1)=0$, and $f^{\prime\prime}(0)=0$
- $f^{\prime\prime}(x) >0$ 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 29:**Complete the following exercises. (Due Wednesday, March 26 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 30:**Read Section Read Section 4.4 and then complete the corresponding problems on WeBWorK. (Due Thursday, March 27 by 11PM)**Daily Homework 31:**Read Section Read Section 4.5 and then complete the corresponding problems on WeBWorK. (Due Friday, March 28 by 11PM)**Daily Homework 32:**Read Section Read Section 4.7 and then complete the corresponding problems on WeBWorK. (Due Thursday, April 3 by 11PM)**Daily Homework 33:**Read Section Read Section 5.1 and then complete the corresponding problems on WeBWorK. (Due Friday, April 4 by 11PM)**Daily Homework 34:**Read Section Read Section 5.2 and then complete the corresponding problems on WeBWorK. (Due Friday, April 11 by 11PM)**Daily Homework 35:**Re-read Section 5.2 and complete the following problems. (Due Monday, April 14 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 36:**Read Section Read Section 5.5 and then complete the corresponding problems on WeBWorK. (Due Wednesday, April 16 by 11PM)**Daily Homework 37:**Read Section Read Section 5.3 and then complete the corresponding problems on WeBWorK. (Due Friday, April 18 by 11PM)**Daily Homework 38:**Read Section Read Section 5.4 and then complete the corresponding problems on WeBWorK. (Due Monday, April 21 by 11PM)**Daily Homework 39:**Read Section Read Section 5.6 and then complete the corresponding problems on WeBWorK. (Due Thursday, April 24 by 11PM)**Daily Homework 40:**Read Section Read Section 5.7 and then complete the corresponding problems on WeBWorK. (Due Wednesday, April 30 by 11PM)

## 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:**Complete the exercises found here (PDF). (Due Friday, January 24 at 9:10AM)**Weekly Homework 2:**Complete the exercises found here (PDF). (Due Thursday, January 30 at 9:10AM)**Weekly Homework 3:**Complete the exercises found here (PDF). (Due Friday, February 7 at 9:10AM)**Weekly Homework 4:**Complete the exercises found here (PDF). (Due Thursday, February 21 at 9:10AM)**Weekly Homework 5:**Complete the exercises found here (PDF). (Due Friday, February 28 at 9:10AM)**Weekly Homework 6:**Complete the exercises found here (PDF). (Due Thursday, March 13 at 9:10AM)**Weekly Homework 7:**Complete the exercises found here (PDF). (Due~~Friday, March 28~~Monday, March 31 at 9:10AM)**Weekly Homework 8:**Complete the exercises found here (PDF). (Due Thursday, April 10 at 9:10AM)