Notes on Oct Midterm

Here's a few notes on the Oct. Midterm

Format/content of exam

Approx 7-8 questions with multiple parts
approx 25-30% of the questions are "basic skills/pre-calc" material
remaining questions will examine functions (Ch 1) and limits and continuity (Ch 2)
no transcendental functions (trig functions, exp, log)
questions will examine factual knowledge (e.g., "give the definition of..."), conceptual knowledge ("prove that f(x) does not have a limit at 0"), and procedural knowledge ('find the roots of a quadratic polynomial')

Review suggestions

Go over WW problems (A1 - A4) - print out the hardcopies and do the problems. Review any material that gives you any difficulty.

Make section summaries of sections 1.1, 1.2, and 2.1-2.7, following the suggestions given in class, in the Wiki at Taking Notes and How To Read Mathematics, including especially the article How to Read Mathematics. These summaries are to be turned in for grading prior to the Midterm

For each definition, give examples of things that satisfy the definition, and things which fail to satisfy the condition. The goal is to find all essential ways in which a definition can fail to be satisfied.

Explain each definition and theorem in your own words.

Some review questions

What is a rational function? How can I compute the domain of a rational function?
What is a difference of squares? How can I simplify expressions involving one?
How do I determine the domain of functions involving square roots?
How can I find the intersection of two curves y=f(x), y=g(x)?
How can I compare two rational functions with different denominators?
What is function composition? If $f(x)=x^{2}$ and $g(x)=2x$ , what is $f\circ g(x)$ ? What is $g\circ f(x)$ ?
How do I compute the limit at infinity of a function?
What is the the absolute value function? What does ${\frac {|x|}{x}}$ look like? What is the limit of this as $x\to 0$ ?
Can I determine the value of a function at a point given its graph?
Can I find the left and right limits of a function at a point by looking at its graph?
What is the "error and tolerance" definition of continuity?
What is the intermediate value theorem (IVT)? How can I use it to tell if a function has a root? What conditions on the function are required?
In what ways can a piecewise function of continuous pieces fail to be continuous?
What is a removable discontinuity? How can I tell without looking at a graph?