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.

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

- Evaluating compositions (Khan Academy), for review, if needed
- Week 1: Intuitive idea of derivatives (Echo360)

- Is the derivative of P positive or negative at t=5 ? Explain.
- Is the second derivative of P positive or negative at t=5 ? Explain.
- Give a value of t where the derivative of P is zero.
- Which day does your tutorial group meet this week?

- Section 3.4 Exponential and Logarithmic Functions, pp. 85-96, from Essential Precalculus, posted to onCourse

- 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.

- All exponential functions \( f(x)=b^x\) share a common point on their graphs. What is it?
- How are the graphs of the functions \( f(x)=2^x\) and \(g(x)=\log_2(x)\) related?
- Solve for x in the equation \(\log_2(x^3-11)=4\).

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

- The Khan Academy Unit on Trigonometry has a lot that you can review. A few that you may want to especially pay attention to are:
- The unit circle definitions of trig functions
- The graph of sin(x) from the unit circle

- Is \( \sin(6\pi / 7) \) positive or negative? Why?
- Is \( \cos(6\pi / 7) \) positive or negative? Why?
- What is the period of the sine function? Why?
- Which day does your tutorial group meet this week?

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

- Limit at a point by Calcvids

- If \( f(x)=x^2\), use the graph of \(y=f(x)\) to explain why \(\displaystyle\lim_{x\to 2} f(x) = 4 \).
- 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.
- Explain why \( \displaystyle\lim_{x\to -3} \frac{x^2-9}{x+3} = -6 \)
- If \( f(x)=x^2\), explain why \( \displaystyle\lim_{h\to 0} \frac{f(5+h) -f(5)}{h} = 10\)
- How is the last question related velocity?

- 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.

- Infinite limits and asymptotes (Khan Academy)

- In Figure 1.4.1, explain why \( \displaystyle\lim_{x\to 1^+}f(x) \ne f(1)\)
- 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? - Give an example of a function that has a vertical asymptote at x = 2. Explain.
- Give an example of a function that has a horizontal asymptote at y = 3. Explain.
- Which day does your tutorial group meet this week?

- Section 2.1 Instantaneous Rates of Change: The Derivative

- Week 4: Definition of the derivative and the derivative of x
^{n}(Echo360)

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

- Section 2.3 Basic Differentiation Rules

- Week 4: Basic differentiation rules (Echo360)

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

- Section 2.4 The Product and Quotient Rules

- Week 5: The product and quotient rules (Echo360)

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

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

- Section 2.5 The Chain Rule

- 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.

- Section 3.1 Extreme Values

- To be updated by 9/22

- Find the critical numbers of \(f(x)\).
- Find the extreme values of \(f(x)\) on the interval \([-1,2]\).