## 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. In addition, complete the corresponding problems on WeBWorK. (Due Thursday, August 29 by 9PM)**Daily Homework 2:**Complete the corresponding problems on WeBWorK. (Due Friday, August 30 by 9PM)**Daily Homework 3:**Complete the corresponding problems on WeBWorK. (Due Wednesday, September 4 by 9PM)**Daily Homework 4:**Complete the corresponding problems on WeBWorK. (Due Thursday, September 5 by 9PM)**Daily Homework 5:**Complete the corresponding problems on WeBWorK. (Due Friday, September 6 by 9PM)**Daily Homework 6:**Complete the corresponding problems on WeBWorK. (Due Monday, September 9 by 9PM)**Daily Homework 7:**Complete the corresponding problems on WeBWorK. (Due Wednesday, September 11 by 9PM)**Daily Homework 8:**Complete the corresponding problems on WeBWorK. (Due Friday, September 13 by 9PM)**Daily Homework 9:**Complete the corresponding problems on WeBWorK. (Due Monday, September 16 by 9PM)**Daily Homework 10:**Complete the corresponding problems on WeBWorK. (Due Wednesday, September 18 by 9PM)**Daily Homework 11:**Read Section 2.7 and 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 and these are due in class). (Due Friday, September 20 by 9PM)- $f(x)=3x^2-x$
- $g(x)=\sqrt{1-x}$

**Daily Homework 12:**Read Sections 3.1 and 3.2. In addition, complete the corresponding problems on WeBWorK. (Due Thursday, September 26 by 9PM)**Daily Homework 13:**Read Section 3.3. In addition, complete the corresponding problems on WeBWorK. (Due Friday, September 27 by 9PM)**Daily Homework 14:**Read Section 3.4 and complete the corresponding problems on WeBWorK. In addition, each group should submit a single worksheet from the work done in class on Friday. (Due Monday, September 30 by 9PM)**Daily Homework 15:**Read Section 3.5 and complete the corresponding problems on WeBWorK. (Due Wednesday, October 2 by 9PM)**Daily Homework 16:**Read Section 3.6 and complete the corresponding problems on WeBWorK. (Due Friday, October 4 by 9PM)**Daily Homework 17:**Read Section 3.7 and complete the corresponding problems on WeBWorK. (Due Monday, October 7 by 9PM)**Daily Homework 18:**Read Section 3.8 and complete the corresponding problems on WeBWorK. (Due Wednesday, October 9 by 9PM)**Daily Homework 19:**Read Sections 3.9 and 3.10 and complete the corresponding problems on WeBWorK. (Due Friday, October 11 by 9PM)**Daily Homework 20:**Read Sections 3.9 and 3.11 and complete the corresponding problems on WeBWorK. (Due Thursday, October 17 by 9PM)**Daily Homework 21:**Read Section 4.1 and complete the corresponding problems on WeBWorK. (Due Friday, October 18 by 9PM)**Daily Homework 22:**Complete the problems on the worksheet distributed in class. Each small group only needs to turn in one assignment. (Due Monday, October 21 in class)**Daily Homework 22:**Read Sections 2.9-2.11 and 4.2 and complete the corresponding problems on WeBWorK. (Due Wednesday, October 23 by 9PM)**Note:**I messed up the homework numbering. There are two assignments called Daily Homework 22.**Daily Homework 23:**Re-read Section 4.2 and complete the corresponding problems on WeBWorK. (Due Thursday, October 25 by 9PM)**Daily Homework 24:**Complete the following exercises. (Due Monday, October 28 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:**Complete the following exercises. (Due Wednesday, October 30 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:**Read Section Read Section 4.4 and then complete the corresponding problems on WeBWorK. (Due Thursday, October 31 by 9PM)**Daily Homework 27:**Read Section Read Section 4.5 and then complete the corresponding problems on WeBWorK. (Due Friday, November 1 by 9PM)**Daily Homework 28:**Read Section Read Section 4.7 and then complete the corresponding problems on WeBWorK. (Due Friday, November 8 by 11PM)**Daily Homework 29:**Read Section Read Section 5.1 and then complete the corresponding problems on WeBWorK. (Due Wednesday, November 13 by 11PM)**Daily Homework 30:**Read Section Read Section 5.2 and then complete the corresponding problems on WeBWorK. (Due Thursday, November 14 by 11PM)**Daily Homework 31:**Re-read Section 5.2 and complete the following problems. (Due Friday, November 15 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 32:**Read Section Read Section 5.5 and then complete the corresponding problems on WeBWorK. (Due Monday, November 18 by 11PM)**Daily Homework 33:**Read Section Read Section 5.3 and then complete the corresponding problems on WeBWorK. (Due Wednesday, November 20 by 11PM)**Daily Homework 34:**Read Section Read Section 5.4 and then complete the corresponding problems on WeBWorK. (Due Friday, November 22 by 11PM)**Daily Homework 35:**Read Section Read Section 5.6 and then complete the corresponding problems on WeBWorK. (Due Monday, November 25 by 11PM)**Daily Homework 36:**Read Section 5.7 and then complete the corresponding problems on WeBWorK. (Due Wednesday, November 27 by 11PM)**Daily Homework 37:**Re-read Section 5.7 and then complete the corresponding problems on WeBWorK. (Due Tuesday, December 3 by 11PM)**Daily Homework 38:**Read Section Read Section 6.1 and then complete the corresponding problems on WeBWorK. (Due Wednesday, December 11 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 Thursday, September 12)**Weekly Homework 2:**Complete the exercises found here (PDF). (Due Thursday, September 19)**Weekly Homework 3:**Complete the exercises found here (PDF). (Due Thursday, October 3)**Weekly Homework 4:**Complete the exercises found here (PDF). (Due Thursday, October 10)**Weekly Homework 5:**Complete the exercises found here (PDF). (Due Thursday, October 24)**Weekly Homework 6:**Complete the exercises found here (PDF). (Due Thursday, November 21)