Homework

Unless a student has a documented excused absence, late homework will not be accepted. There are many resources available to assist you with doing your homework (e.g., office hours, course Google Group, free tutoring at numerous places across campus). You are allowed and encouraged to work together on homework. However, each student is expected to turn in his or her own work.

Daily Homework

The Daily Homework will generally consist of solving problems from the IBL course notes (PDF). On the day that a homework assignment is due, the majority of the class period will be devoted to students presenting some subset (maybe all) of the solutions/proofs that are due that day. Students are allowed (in fact, encouraged!) to modify their written solutions in light of presentations made in class; however, you are required to use the colored marker pens provided in class.

  • 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. (Due Wednesday, August 27)
  • Daily Homework 2: Read the Introduction to Differential Calculus (PDF). In addition, read Chapter 0 up to Problem 11 and complete Problems 3-11. (Due Wednesday, August 27)
  • Daily Homework 3: Stop by my office (AMB 176) and say hello. If I’m not there, just slide note under my door saying you stopped by. (Due Friday, August 29 by 5PM)
  • Daily Homework 4: Read the rest of Chapter 0 in Differential Calculus and complete Problems 12, 14, 15, 17-19. (Due Friday, August 29)
  • Daily Homework 5: Read Chapter 1 up to Problem 32 in Differential Calculus and complete Problems 21-29, 31, 32. Hint: Problem 25 is hinting at tangent lines (see Definition 30). (Due Wednesday, September 3)
  • Daily Homework 6: Read the rest of Chapter 1 and complete Problems 33-35, 37-41. Hints: For Problem 34, use Problem 26 and the idea from Problem 25. For Problem 35 use the same approach as Problem 34. For Problems 37 and 38, use Problems 33 and 34, respectively. (Due Thursday, September 4)
  • Daily Homework 7: Read the rest of Chapter 1 and Chapter 2 up to Problem 54. In addition, complete Problems 43-45, 47-54. Note: For Problems 47-54, feel free to utilize technology to graph the functions, but you should also attempt to explore the functions algebraically. (Due Friday, September 5)
  • Daily Homework 8: Read Chapter 2 up to Theorem 68. In addition, complete Problems 56-58, 66, 67. Also, read Theorem 68 and try to draw to picture that captures its meaning. Hint: For the third part of Problem 67, look up the formula for factoring a difference of two cubes. (Due Wednesday, September 10)
  • Daily Homework 9: Read the rest of Chapter 2. In addition, complete Problems 69-75. For Problem 69, you should just look up the answer (e.g., use a Google search). Hints: For Problem 72, you cannot “pull the 4 out of the sine function”. However, a key observation is that $4\theta\to 0$ as $\theta\to 0$. For Problem 73, consider multiplying the expression by $4/4$. For Problem 74, consider multiplying by the conjugate and using a relevant trig identity. For Problem 75, use the Sandwich/Squeeze Theorem. (Due Thursday, September 11)
  • Daily Homework 10: Read Chapter 3 up to Problem 85. In addition, complete Problems 78, 80, 81, 83-85. (Due Friday, September 12)
  • Daily Homework 11: Read Chapter 3 up to Problem 89. In addition, complete Problems 86, 88, 89. Also, complete the statement of Theorem 87. (Due Monday, September 15)
  • Daily Homework 12: Complete Exercises 2.5.5, 2.5.6, and 2.5.8 in Calculus I Lecture Notes. (Due Wednesday, September 17)
  • Daily Homework 13: Complete practice problems 4 and 5 from the Chapters 1-2 Review from Calculus I Lecture Notes. (Due Thursday, September 18)
  • Daily Homework 14: Read Chapter 3 up to Problem 93. In addition, complete Problems 90, 92, 93. Also, complete the statement of Theorem 91. (Due Monday, September 22)
  • Daily Homework 15: Complete Problems 132-134, 136(a)(b), 139, 141, 142. Also, complete the statement of Theorems 135 and 140 along the way. (Due Wednesday, September 24)
  • Daily Homework 16: Complete Problems 121, 125-129, 136(c), 137, 138. Hints: To do 125 and 126, you will need Theorem 124. Also, it may be useful to know that $$\frac{d}{dx}[\sin(x)]=\cos(x)$$ and $$\frac{d}{dx}[\cos(x)]=-\sin(x).$$
    To compute the derivatives of the functions for Problem 137, you should use the derivatives that I just mentioned and the quotient rule. (Due Friday, September 26)
  • Daily Homework 17: Complete Problems 149-153. Hints: It will be useful to know that $$\frac{d}{dx}[e^x]=e^x$$ and $$\frac{d}{dx}[b^x]=b^x\ln(b).$$
    You’ll prove that the first formula is correct in Problem 150. For now, you can just assume that the second formula is correct. (Due Monday, September 29)
  • Daily Homework 18: Complete Problems 160, 163-166. Hints: It will be useful to know that for $x>0$ $$\frac{d}{dx}[\ln(x)]=\frac{1}{x}$$ and $$\frac{d}{dx}[\log_b(x)]=\frac{1}{x\ln(b)}.$$ Also, when the author of the notes writes $\overline{f}$, you should just write $f^{-1}$. (Due Wednesday, October 1)
  • Daily Homework 19: Complete Exercises 3.10.2 and 3.10.3 from Calculus I Lecture Notes. (Due Friday, October 3)
  • Daily Homework 20: Complete Exercises 3.11.2 and 3.11.3 from Calculus I Lecture Notes. (Due Wednesday, October 8)
  • Daily Homework 21: Complete any 10 problems from 15-38 in Section 3.13 of Calculus I Lecture Notes. (Due Thursday, October 9)
  • Daily Homework 22: Complete all 11 parts of Exercise 4.1.6 in Section 4.1 of Calculus I Lecture Notes. (Due Wednesday, October 15)
  • Daily Homework 23: Complete Problems 94, 97-100, 102, 103 in Differential Calculus (PDF). Also, digest the relevant definitions nearby. (Due Thursday, October 16)
  • Daily Homework 24: Complete Problems 104-113 in Differential Calculus (PDF). (Due Friday, October 17)
  • Daily Homework 25: Complete Problems 114-119 in Differential Calculus (PDF). (Due Monday, October 20)
  • Daily Homework 26: Complete the following exercises. (Due Thursday, October 23)
    1. 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 $(0,3)$
    2. Sketch the graph of the following functions by following the algorithm we discussed in class.
      • $f(x) = \displaystyle \frac{x^2}{x-2}$
      • $g(x) = \displaystyle xe^x$
  • Daily Homework 27: Complete the following exercises. (Due Friday, October 24)
    1. 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.
    2. Sketch the graph of a function on $[1,4]$ that has an absolute max but no absolute min.
    3. Sketch the graph of a function on $[1,4]$ that is not continuous but has both an absolute max and an absolute min.
    4. 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 corresponding problems on WeBWorK. (Due Monday, October 27 by 8:00pm)
  • Daily Homework 29: Complete Problems 167-169 in Differential Calculus (PDF). In addition, complete any 4 parts of Exercise 4.5.3 in Section 4.5 of Calculus I Lecture Notes. (Due Wednesday, October 29)
  • Daily Homework 30: Complete Problems 179-183 in Differential Calculus (PDF). (Due Wednesday, November 5)
  • Daily Homework 31: Complete Problems 185-197 in Differential Calculus (PDF). (Due Thursday, November 6)
  • Daily Homework 32: Complete Problems 198, 200-204, 206-208 in Differential Calculus (PDF). (Due Friday, November 7)
  • Daily Homework 33: Complete Problems 211-216 in Differential Calculus (PDF). (Due Monday, November 10)
  • Daily Homework 34: Complete Problems 218-224 in Differential Calculus (PDF). (Due Thursday, November 13)
  • Daily Homework 35: Complete Problems 225-227 in Differential Calculus (PDF). In addition, complete the following. (Due Thursday, November 13)
    1. 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.
    2. Compute the value of $\displaystyle \int_0^1 x^2-4x\ dx$ using a limit of Riemann sums and right endpoints.
  • Daily Homework 36: Complete Problems 228-232 in Differential Calculus (PDF). (Due Monday, November 17)
  • Daily Homework 37: Complete Problems 233-236 in Differential Calculus (PDF). (Due Wednesday, November 19)
  • Daily Homework 38: Complete Exercises 5.6.5(5) and 5.6.6 in Section 5.6 of Calculus I Lecture Notes. In addition, complete exercises 17-19, 35, plus any 4 more from Section 5.8 of Calculus I Lecture Notes. (Due Thursday, November 20)
  • Daily Homework 39: Complete Exercises 5.7.5 (replace $\sinh(x)$ with $\sin(x)$ on part 4), 5.7.7, 5.7.10, 5.7.11 in Section 5.7 of Calculus I Lecture Notes. (Due Friday, November 21)
  • Daily Homework 40: Complete corresponding problems on WeBWorK. Be sure to also complete the problems on paper as we will be presenting the problems on Wednesday. (Due by 9:10am on Thursday, December 4)

Weekly Homework

The majority of the Weekly Homework assignments are to be completed via WeBWorK, which is an online homework system. You should log in with your NAU credentials.

  • Weekly Homework 1: Complete the corresponding problems on WeBWorK. (Due Tuesday, September 2 by 5PM)
  • Weekly Homework 2: Complete the corresponding problems on WeBWorK. (Due Tuesday, September 9 by 8PM)
  • Weekly Homework 3: Complete the corresponding problems on WeBWorK. (Due Tuesday, September 16 by 8PM)
  • Weekly Homework 4: Complete the corresponding problems on WeBWorK. (Due Tuesday, September 30 by 8PM)
  • Weekly Homework 5: Complete the corresponding problems on WeBWorK. (Due Tuesday, October 7 by 8PM)
  • Weekly Homework 6: Complete the corresponding problems on WeBWorK. (Due Tuesday, October 20 by 8PM)
  • Weekly Homework 7: Complete the corresponding problems on WeBWorK. (Due Tuesday, October 28 by 8PM)
  • Weekly Homework 8: Complete the corresponding problems on WeBWorK. (Due Wednesday, November 12 by 8PM)
  • Weekly Homework 9: Complete the corresponding problems on WeBWorK. (Due Tuesday, November 18 by 8PM)
  • Weekly Homework 10: Complete the corresponding problems on WeBWorK. (Due Monday, November 24 by 9PM)