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

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.

• Since the main text doesn't include background material on exponentials, logarithms, or trig functions, I posted references for the first two weeks of class to onCourse.
• Beginning on Monday September 7, all numbers indicate sections from APEX Calculus, Version 4.0.
Be sure to check the Errata for corrections to the text.

### Due Tuesday August 25 @ midnight

#### An intuitive introduction to derivatives

• Section 1.4 Amount Functions and Rate Functions: The Idea of the Derivative, from Ostebee/Zorn, pp. 35-44, posted to onCourse
##### 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?

### Due Sunday August 30 @ midnight

#### Review of exponentials and logarithms

• Section 3.4 Exponential and Logarithmic Functions, pp. 85-96, from Essential Precalculus, posted to onCourse
##### To Watch
• The Khan Academy Unit on Logarithms has lots of relevant videos, depending on how much you need to review. Specifically, these might be worth reviewing if you're feeling a little rusty.

#### 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 $$\log_2(x^3-11)=4$$.

### Due Tuesday September 1 @ midnight

#### Review of trigonometric functions

• Section 4.1 The Unit Circle: Sine and Cosine, from Essential Precalculus, posted to onCourse

#### 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?

### Due Sunday September 6 @ midnight

#### Finding limits graphically and analytically

• Section 1.1 An Introduction to Limits
• Section 1.3 Finding Limits Analytically
• Section 1.4 One Sided Limits

#### 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?

### Due Tuesday September 8 @ midnight

#### Continuity and limits at infinity

• Section 1.5 Continuity
• Section 1.6 Limits Involving Infinity

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.

#### 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?

### Due Sunday September 13 @ midnight

#### The derivative

• Section 2.1 Instantaneous Rates of Change: The Derivative
##### To Watch
• Week 4: Definition of the derivative and the derivative of xn (Echo360)

#### 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.

### Due Tuesday September 15 @ midnight

#### Finding formulas for derivatives

• Section 2.3 Basic Differentiation Rules
##### To Watch
• Week 4: Basic differentiation rules (Echo360)

#### 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?

### Due Sunday September 20 @ midnight

#### The product and quotient rules

• Section 2.4 The Product and Quotient Rules
##### To Watch
• Week 5: The product and quotient rules (Echo360)

#### 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 $$f'(x)=\displaystyle\frac{2x+7}{4x^3+10x}$$.

### For Tuesday September 22 @ midnight

#### The chain rule

• Section 2.5 The Chain Rule
##### To Watch
• How to Use the Chain Rule by Calcvids
Don't get hung up on the derivative of r(x) in the video - we'll talk about derivatives of logarithms other than ln(x) later.
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

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 $$[-1,2]$$.