Math 161 Calculus I

Reading Outlines

You should write down answers to these questions as you read the text.

Section 2.6

1. Explain what a limit is, in your own words.
2. Let g(x) = (x² - 9)/(x - 3) as in Example 2.
   1. Is g(x) defined at x = 3? Why or why not?
   2. What is $\lim_{x\rightarrow 3}^{}$g(x)? Why?
3. Does f (a) need to be defined for $\lim_{x\rightarrow a}^{}$f (x) to exist? Explain and give an example to support your answer.
4. What kinds of limits have we been computing in this class? Why did I ask the question above?
5. What does the $\epsilon$ in the formal definition of limit correspond to in the informal definition? What about the $\delta$?
6. Draw another function (besides | x|) which has a point at which the derivative isn't defined.
7. Is n(x) in Example 8 continuous at x = - 3? Why or why not?
8. What does continuity have to do with limits?
9. What's a point of discontinuity of a function?