Pre-Class Assignments, Math 101 Calculus I, Fall 2020

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Be sure to check back, because this page will be updated often during the semester.


Due Tuesday August 25 @ midnight

An intuitive introduction to derivatives

To Read
To Watch
Links in "Echo360 and other course videos" topic in onCourse. ~10 minutes total

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.
  4. Which day does your tutorial group meet this week?
Submit answers through onCourse

Due Sunday August 30 @ midnight

Review of exponentials and logarithms

To Read
To Watch

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. Solve for x in the equation \(\log_2(x^3-11)=4\).
Submit answers through onCourse

Due Tuesday September 1 @ midnight

Review of trigonometric functions

To Read
To Watch

Pre-Class Questions

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?
  3. What is the period of the sine function? Why?
  4. Which day does your tutorial group meet this week?
Submit answers through onCourse

Due Sunday September 6 @ midnight

Finding limits graphically and analytically

To Read
To Watch

Pre-Class Questions

  1. If \( f(x)=x^2\), use the graph of \(y=f(x)\) to explain why \(\displaystyle\lim_{x\to 2} f(x) = 4 \).
  2. If \( f(x)=\displaystyle\frac{1}{x}\), use the graph of \(y=f(x)\) to explain why \(\displaystyle\lim_{x\to 0} f(x)\) does not exist.
  3. Explain why \( \displaystyle\lim_{x\to -3} \frac{x^2-9}{x+3} = -6 \)
  4. If \( f(x)=x^2\), explain why \( \displaystyle\lim_{h\to 0} \frac{f(5+h) -f(5)}{h} = 10\)
  5. How is the last question related velocity?
Submit answers through onCourse

Due Tuesday September 8 @ midnight

Continuity and limits at infinity

To Read

Don't worry about the references to the \(\epsilon - \delta\) definition of the limit in these sections, but try to use your graphical intuition about limits.

To Watch

Pre-Class Questions

  1. In Figure 1.4.1, explain why \( \displaystyle\lim_{x\to 1^+}f(x) \ne f(1)\)
  2. How can you tell from the graph of y=f(x) if the function f(x) is continuous?
  3. Why is the Intermediate Value Theorem called the Intermediate Value Theorem?
  4. Give an example of a function that has a vertical asymptote at x = 2. Explain.
  5. Give an example of a function that has a horizontal asymptote at y = 3. Explain.
  6. Which day does your tutorial group meet this week?
Submit answers through onCourse

Due Sunday September 13 @ midnight

The derivative

To Read
To Watch

Pre-Class Questions

  1. Let \( f(x)=3x^2\). Find \( f'(2)\).
  2. Use the graph of \(f(x)=|x|\) to explain why \( f'(0)\) does not exist.
Submit answers through onCourse

Due Tuesday September 15 @ midnight

Finding formulas for derivatives

To Read
To Watch

Pre-Class Questions

  1. If \(f(x)=x^8+\frac{1}{x}-\sin(x)+3\cos(x)\), what is \(f'(x)\)?
  2. If \(g(x)=e^x\), what is the 42nd derivative of \(g(x)\)?
  3. Which day does your tutorial group meet this week?
Submit answers through onCourse

Due Sunday September 20 @ midnight

The product and quotient rules

To Read
To Watch

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 \( f'(x)=\displaystyle\frac{2x+7}{4x^3+10x}\).
Submit answers through onCourse

For Tuesday September 22 @ midnight

The chain rule

To Read
To Watch
No questions to submit today because of Exam 1

For Sunday September 27

Putting it all together

Review the techniques of differentiation, but no questions to submit for today.

Due Tuesday September 29 @ midnight

Extreme values

To Read
To Watch

Pre-Class Questions

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 \([-1,2]\).
Submit answers through onCourse