T. Ratliff Home  |  Math Home  |   Wheaton Home

Pre-Class Assignments, Math 101 Calculus I, Fall 2024

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 this page will be updated often during the semester.

Week 1: Before class meeting on Friday August 30

An intuitive introduction to derivatives

To Read

Optional videos from Fall 2020

Pre-Class Questions

Look at the graphs of P(t) and V(t) in Figure 1 on page 37.
  1. Is the derivative of P positive or negative at t=5 ? Explain.
  2. Is the second derivative of P positive or negative at t=5 ? Explain.
  3. Give a value of t where the derivative of P is zero.

Think about these, but no need to submit answers this first week.

Week 2: Due Tuesday September 3 @ 11:59 pm

Review of exponentials, logarithms, and trigonometric functions

To Read

Optional videos from Fall 2020

Pre-Class Questions

  1. All exponential functions \( f(x)=b^x\) share a common point on their graphs. What is it?
  2. How are the graphs of the functions \( f(x)=2^x\) and \(g(x)=\log_2(x)\) related?
  3. Use the unit circle definitions of sine and cosine to answer the following.
    1. Is \( \sin(6\pi / 7) \) positive or negative? Why?
    2. Is \( \cos(6\pi / 7) \) positive or negative? Why?

Submit answers through Canvas

Week 3: Due Tuesday September 10 @ 11:59 pm

Limits and continuity

To Read

Note that these sections are from APEX Calculus.

This is the longest assignment of the semester by far. Try to read/skim these sections for the main ideas, and don't get too hung up in the details in your first reading. We'll discuss all the most important points thoroughly during class. You can also ignore any references to the ε - δ definition of the limit in these sections.

Optional videos from Fall 2020

Pre-Class Questions

  1. Explain why \( \displaystyle\lim_{x\to -3} \frac{x^2-9}{x+3} = -6 \)
  2. If \( f(x)=x^2\), explain why \( \displaystyle\lim_{h\to 0} \frac{f(5+h) -f(5)}{h} = 10\)
  3. In Figure 1.4.1, explain why \( \displaystyle\lim_{x\to 1^+}f(x) \ne f(1)\)
  4. How can you tell from the graph of y=f(x) if the function f(x) is continuous?

Submit answers through Canvas

Week 4: Due Sunday September 15 @ 11:59 pm

Asymptotes
The definition of the derivative
Basic differentiation rules

To Read

Optional videos from Fall 2020

Pre-Class Questions

  1. Give an example of a function that has a vertical asymptote at x = 3. Explain.
  2. Let \( f(x)=3x^2\). Use the limit definition of the derivative (Definition 2.1.1 on page 62) to find \( f'(2)\).
  3. Use the graph of \(f(x)=|x|\) to explain why \( f'(0)\) does not exist.
  4. If \(f(x)=x^8+\frac{1}{x}-\sin(x)+3\cos(x)\), what is \(f'(x)\)?

Submit answers through Canvas

Week 5: Before class on Friday September 27

The product and quotient rules

To Read

Optional videos from Fall 2020

Pre-Class Questions

Explain what is wrong with the following calculations and fix them.
  1. If \( f(x)=(x^2+7x)(x^4 + 5 x^2 + 9)\), then \( f'(x)=(2x+7)(4x^3+10x)\).

  2. If \( f(x)=\displaystyle\frac{x^2+7x}{x^4 + 5 x^2 + 9}\), then \( f'(x)=\displaystyle\frac{2x+7}{4x^3+10x}\).

Think about these, but no need to submit your answers. Focus on prepping for Exam 1.

Week 6: Before class on Monday September 30

The Chain rule
Extreme values

To Read

Optional videos from Fall 2020

Pre-Class Questions

  1. Explain what is wrong with the following calculation and fix it: If \(f(x)=(x^2+2x)^{130}\), then \(f'(x)=130(x^2+2x)^{129}\).
  2. Let \(f(x)=2x^3+3x^2-12x+5\).
    1. Find the critical numbers of \(f(x)\).
    2. Find the extreme values of \(f(x)\) on the interval \([-1,2]\).

Think about these, but no need to submit your answers. Focus on the takehome part of Exam 1.

Week 7: Due Sunday October 6 @ 11:59 pm

The Mean Value Theorem
The second derivative & concavity

To Read

Optional videos from Fall 2020

Pre-Class Questions

  1. What is an important consequence of the Mean Value Theorem related to finding antiderivatives of a function f(x)?
  2. Let f(x)=x3-3x2-9x+7.
    1. Find the critical numbers of f(x)
    2. Find the intervals where f(x) is increasing and the intervals where f(x) is decreasing
    3. Use the First Derivative Test to identify each critical number as a relative maximum, minimum, or neither
  3. Using the same function f(x) as in #2,
    1. Find the inflection points of f(x)
    2. Find the intervals where f(x) is concave up and the intervals where f(x) is concave down
    3. Use the Second Derivative Test to identify each critical number of f(x) as a relative maximum or minimum, if possible.

Submit answers through Canvas

Week 8: Due Tuesday October 15 @ 11:59 pm

More with concavity
L'Hôpital's Rule

To Read

Optional videos from Fall 2020

Pre-Class Questions

  1. Is the limit \( \displaystyle \lim_{x \to \infty} \frac{e^x}{x} \) in indeterminate form? Explain.
  2. Is the limit \( \displaystyle \lim_{x \to 0} \frac{\cos(3x)}{x} \) in indeterminate form? Explain.

Submit answers through Canvas

Week 9: Due Sunday October 20 @ 11:59 pm

Optimization
Taylor Polynomials

To Read

Optional videos from Fall 2020

Pre-Class Questions

  1. What is the purpose of finding the Taylor polynomial for a known function like \(f(x)=\sin(x)\)?
  2. What is the difference between a Taylor polynomial and a Maclaurin polynomial?

Submit answers through Canvas

Week 10: Before class meeting on Friday November 1

Antiderivatives and the indefinite integral

To Read

Optional videos from Fall 2020

Pre-Class Questions

  1. Give two antiderivatives to \( f(x)= 2x + \cos(x)\)
  2. Evaluate \( \displaystyle\int 2x + \cos(x) dx\)

Think about these, but no need to submit your answers. Focus on prepping for Exam 2.

Week 11: Before class on Monday November 4

The definite integral
Riemann sums
The Fundamental Theorem of Calculus

To Read

Optional videos from Fall 2020

Pre-Class Questions

  1. What is the difference between a definite integral and an indefinite integral?
  2. Look at graph in Figure 5.2.8 on pg 213. Will \(\displaystyle \int_0^a f(t) dt\) be positive or negative? How about \(\displaystyle\int_0^b f(t) dt\)? Explain.
  3. What is the purpose of a Riemann sum?
  4. Will a Right Hand Rule sum overestimate or underestimate \(\displaystyle\int_0^2 x^2 dx\)? Explain.

Think about these, but no need to submit your answers. Focus on the takehome part of Exam 2.

Week 12: Due Sunday November 10 @ 11:59 pm

FTC! FTC!
\( u \)-substitution

To Read

Optional videos from Fall 2020

Pre-Class Questions

  1. Substitution attempts to undo one of the techniques of differentiation. Which one is it?
  2. Use \(u\)-substitution to find an antiderivative of \(f(x) = 3x^2\cos(x^3)\)

Submit answers through Canvas

Week 13: Before class on Friday November 22

Modeling and applications

Optional videos from Fall 2020

Pre-Class Questions

  1. Why is a logistic model more accurate than an exponential model when modeling an epidemic?
  2. Around the 5:00 mark of the "Exponential growth and epidemics" video, they mark a point as an inflection point. Explain why this point matches our calculus definition of an inflection point being a place where the second derivative is 0.

Think about these, but no need to submit your answers. Focus on prepping for Exam 3.

Week 14: No additional pre-class prep

Focus on the takehome part of Exam 3.

Week 15: No additional pre-class prep

For the last week of the semester we'll be reviewing and looking at the Big Picture of Calculus I. No Pre-Class Assignment for this week.


Maintained by: ratliff_thomas@wheatoncollege.edu