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This page uses MathJax to display mathematical notation, so please let me know if any part isn't clear.
Be sure to check back, because there will certainly be some changes during the semester.
All numbers indicate sections from
APEX Calculus, Version 3.0, and check the
Errata for corrections to the text.
For Friday September 1 (Due 8/31 @ 8:00 pm)
Review of Exponential and Logarithmic Functions
To watch
The text doesn't include background material on exponential or logarithmic functions, so these are some videos that should serve as a good review. They were done by Ed Berger, formerly of Williams Collage and currently president of Southwestern University in Georgetown, Texas.
Depending on how comfortable you are with this material, you may be able to skip through parts of these. Also feel free to look for your own resources!
- Exponential Functions
- Logarithmic Functions
"Reading" Questions
- How are the graphs of the functions \( f(x)=2^x\) and \(g(x)=\log_2(x)\) related?
- Solve for x in the equation \(\log_2(x) + \log_2(x^3)=4\).
Submit answers through onCourse
For Monday September 4
Labor Day. No class meeting or reading assignment due.
For Wednesday September 6 (Due 9/5 @ 8:00 pm)
Review of Trigonometric Functions
To watch
As above, depending on how comfortable you are with this material, you may be able to skip through parts of these.
"Reading" Questions
- What is 120 degrees equal to in radians?
- What is the period of the sine function? How can you tell from the graph?
Submit answers through onCourse
For Friday September 8 (Due 9/7 @ 8:00 pm)
Section 1.1 An Introduction to Limits
Reading Questions
- If \( f(x)=x^2\), explain why \(\dst\lim_{x\to 2} f(x) = 4 \).
- If \( f(x)=\dst\frac{1}{x}\), explain why \(\dst\lim_{x\to 0} f(x)\) does not exist.
- How is the difference quotient related to calculus?
Submit answers through onCourse
For Monday September 11 (Due 9/10 @ 8:00 pm)
Section 1.3 Finding Limits Analytically
You can de-emphasize the section on the Squeeze Theorem.
Reading Questions
- Explain why \( \dst\lim_{x\to -3} \frac{x^2-9}{x+3} = -6 \)
- If \( f(x)=x^2\), explain why \( \dst\lim_{h\to 0} \frac{f(5+h) -f(5)}{h} = 10\)
- How is the last question related velocity?
Submit answers through onCourse
For Wednesday September 13 (Due 9/12 @ 8:00 pm)
Section 1.4 One Sided Limits
Section 1.5 Continuity
In Section 1.4, do not worry about the references to the \(\epsilon - \delta\) definition of the limit,
but try to think about the intuition behind one sided limits.
Reading Questions
- In Figure 1.21, explain why \( \dst\lim_{x\to 1^+}f(x) \ne f(1)\)
- How can you tell from the graph of y=f(x) if the function f(x) is continuous?
- Why is the Intermediate Value Theorem called the Intermediate Value Theorem?
Submit answers through onCourse
For Friday September 15 (Due 9/14 @ 8:00 pm)
Section 1.6 Limits Involving Infinity
Do not worry about the references to the \(\epsilon - \delta\) definition of the limit.
Reading Questions
- Give an example of a function that has a vertical asymptote at x = 3. Explain.
- Give an example of a function that has a horizontal asymptote at y = 3. Explain.
Submit answers through onCourse
For Monday September 18 (Due 9/17 @ 8:00 pm)
Section 2.1 Instantaneous Rates of Change: The Derivative
Reading Questions
- Let \( f(x)=3x^2\). Find \( f'(2)\).
- Use the graph of \(f(x)=|x|\) to explain why \( f'(0)\) does not exist.
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For Wednesday September 20 (Due 9/19 @ 8:00 pm)
Section 2.2 Interpretations of the Derivative
Reading Questions
Let \(T(h)\) give the temperature in degrees Farenheit in Norton \(h\) hours after midnight on May 20, 2017.
- What are the units for \(T'(h)\)?
- Do you think \(T'(10)\) is positive or negative? Explain.
- Do you think \(T(10)\) is positive or negative? Explain.
Submit answers through onCourse
For Friday September 22 (Due 9/21 @ 8:00 pm)
Section 2.3 Basic Differentiation Rules
Reading Questions
- If \(f(x)=x^8+2x^2\), what is \(f'(x)\)?
- If \(g(x)=e^x\), what is the 42nd derivative of \(g(x)\)?
Submit answers through onCourse
For Monday September 25
Section 2.3 Basic Differentiation Rules
Re-read the section, but no Reading Questions for today.
For Wednesday September 27
Q & A for Exam 1. No reading assignment.
For Friday September 29 (Due 9/28 @ 8:00 pm)
Section 2.4 The Product and Quotient Rules
Reading Questions
Explain what is wrong with the following calculations and fix them.
- If \( f(x)=(x^2+7x)(x^4 + 5 x^2 + 9)\), then \( f'(x)=(2x+7)(4x^3+10x)\).
- If \( f(x)=\dst\frac{x^2+7x}{x^4 + 5 x^2 + 9}\), then \( f'(x)=\dst\frac{2x+7}{4x^3+10x}\).
Submit answers through onCourse
For Monday October 2 (Due 10/1 @ 8:00 pm)
Section 2.5 The Chain Rule
Reading Questions
Explain what is wrong with the following calculations and fix them.
- If \(f(x)=(x^2+2x)^{130}\), then \(f'(x)=130(x^2+2x)^{129}\).
- If \(f(x)=\sin(x^2)\), then \(f'(x)=\cos(2x)\).
Submit answers through onCourse
For Wednesday October 4
Section 2.5 The Chain Rule
Re-read the section, but no Reading Questions for today.
For Friday October 6 (Due 10/5 @ 8:00 pm)
Section 3.1 Extreme Values
Reading Questions
Let \(f(x)=2 x^3-3 x^2-12 x+1\).
- Find the critical numbers of \(f(x)\).
- Find the extrema of \(f(x)\) on the interval \([-2,1]\).
Submit answers through onCourse
For Monday October 9
Fall Break. No class meeting or reading assignment due.
For Wednesday October 11 (Due 10/10 @ 8:00 pm)
Section 3.2 The Mean Value Theorem
You can skip the proofs of the Mean Value Theorem and Rolle's Theorem.
Reading Questions
- Explain the Mean Value Theorem using "car talk" (that is, in terms of velocity).
- Consider \(f(x)=5 x^3 - 2 x\). Find \(c\) in \([1,4]\) that satisfies the Mean Value Theorem.
Submit answers through onCourse
For Friday October 13 (Due 10/12 @ 8:00 pm)
Section 3.3 Increasing and Decreasing Functions
Reading Questions
Let \(f(x)=\dst\frac{x^5}{5}-\frac{x^4}{4}-\frac{2 x^3}{3}+3\)
- Verify that \(x=-1\), \(x=0\), and \(x=2\) are the critical numbers of \(f(x)\).
- Find the intervals where \(f(x)\) is increasing and decreasing.
- Use the First Derivative Test to identify each critical number as a relative maximum, minimum, or neither.
Submit answers through onCourse
For Monday October 16 (Due 10/15 @ 8:00 pm)
Section 3.4 Concavity and the Second Derivative
Reading Questions
Let \(f(x)=\dst\frac{x^5}{5}-\frac{x^4}{4}-\frac{2 x^3}{3}+3\). Notice this is the same function from Friday.
- Verify that \(x=0\), \(x=\dst\frac{1}{8} \left(3-\sqrt{73}\right)\), and \(x=\dst\frac{1}{8} \left(3+\sqrt{73}\right)\)
could be inflection points of \(f(x)\).
- Find the intervals where \(f(x)\) is concave up and concave down.
- Use the Second Derivative Test to identify each critical number of \(f(x)\)
as a relative maximum or minimum, if possible.
Submit answers through onCourse
For Wednesday October 18
Section 3.5 Curve Sketching
Read all of this section and pay special attention to Examples 93, 94, and 95, but no Reading Questions for today.
For Friday October 20 (Due 10/19 @ 8:00 pm)
Section 4.3 Optimization
Reading Questions
Consider the following problem: Find the minimum sum of two non-negative numbers, \(a\) and \(b\), whose product is 100.
- Write the quantity to be optimized in terms of \(a\) and \(b\). The text calls this the "fundamental equation."
- Write the quantity from 1 in terms of just \(a\).
- How do you use the expression in 2 to find the minimum sum?
Submit answers through onCourse
For Monday October 23
Section 4.3 Optimization
Re-read the section, but no Reading Questions for today.
For Wednesday October 25 (Due 10/24 @ 8:00 pm)
Section 8.7 Taylor Polynomials
You can de-emphasize the parts related to bounding the error \( R_n(x)\) described in Theorem 76.
Reading Questions
- What is the purpose of finding the Taylor polynomial for a known function like \(f(x)=\sin(x)\)?
- In your own words, explain the basic concept underlying the construction of a Maclaurin polynomial in a few sentences.
Submit answers through onCourse
For Friday October 10/27
Flex Day. No reading assignment.
For Monday October 30 (Due 10/29 @ 8:00 pm)
Section 5.1 Antiderivatives and Indefinite Integration
Reading Questions
- Evaluate \( \int 2x + \cos(x) dx\)
- Verify that \( \int \ln(x) dx = x\ln(x)-x+C\)
- Find \(f(x)\) given that \( f'(x)=x^2\) and \( f(2)=3\)
Submit answers through onCourse
For Wednesday November 1
Q & A for Exam 2. No reading assignment.
For Friday November 3
Section 5.1 Antiderivatives and Indefinite Integration
Re-read the section, but no Reading Questions for today.
For Monday November 6 (Due 11/5 @ 8:00 pm)
Section 5.2 The Definite Integral
Reading Questions
- What is the difference between a definite integral and an indefinite integral?
- Look at graph in Figure 5.9 on pg 205. Will \( \int_0^a f(t) dt\) be positive or negative?
How about \(\int_0^b f(t) dt\)? Explain.
Submit answers through onCourse
For Wednesday November 8
Section 5.2 The Definite Integral
Re-read the section, but no Reading Questions for today.
For Friday November 10 (Due 11/9 @ 8:00 pm)
Section 5.3 Riemann Sums
Reading Questions
- What is the purpose of a Riemann sum?
- Will a Right Hand Rule sum overestimate or underestimate \(\int_0^2 x^2 dx\)? Explain.
Submit answers through onCourse
For Monday November 13 (Due 11/12 @ 8:00 pm)
Section 5.4 The Fundamental Theorem of Calculus
Reading Questions
- Does every continuous function have an antiderivative? Why or why not?
- Find the area of the region above the \(x\)-axis and below the graph of
\( f(x)= \dst\frac{4}{x} + \cos(x) + 1\) between \(x=1\) and \(x=10\).
Submit answers through onCourse
For Wednesday November 15
Section 5.4 The Fundamental Theorem of Calculus
Re-read the section, but no Reading Questions for today.
For Thursday November 16
Section 5.5 Numerical Integration
You should think about these questions while reading, but you do not need to submit answers.
Reading Questions
- Why would you ever want to numerically approximate an integral?
- Which would you expect to be MOST accurate: a Right Hand approximation, a Trapezoidal approximation, or a Simpson's approximation? Explain.
- Which would you expect to be LEAST accurate: a Right Hand approximation, a Trapezoidal approximation, or a Simpson's approximation? Explain.
Submit answers through onCourse
For Monday November 11/20
Section 5.5 Numerical Integration
Re-read the section, but no Reading Questions for today.
For Wednesday November 22
Thanksgiving Break. No class meetings or reading assignments due.
For Friday November 24
Thanksgiving Break. No class meetings or reading assignments due.
For Monday November 27 (Due 11/26 @ 8:00 pm)
Section 6.1 Substitution
You can skip the parts related to the inverse trig functions.
Reading Questions
- Substitution attempts to undo one of the techniques of differentiation. Which one is it?
- Use \(u\)-substitution to find an antiderivative of \(f(x) = 3x^2\cos(x^3)\)
- Explain why \( \int\cos(x) \sin(x)^2\ dx\) and \(\dst\int \frac{\ln(x)^2}{x}\ dx\) are
essentially the same integral after performing a substitution.
Submit answers through onCourse
For Wednesday November 29
Q & A for Exam 3. No reading assignment.
For Friday December 1
Section 6.1 Substitution
Re-read the section, but no Reading Questions for today.
For Monday December 4
Section 6.1 Substitution
Re-read the section, but no Reading Questions for today.
For Wednesday December 6
The Big Picture. No reading assignment for today.
For Friday December 8
The Big Picture. No reading assignment for today.
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