Reading Assignments for Calculus I
    Fall 1999, Math 101

    CHAPTER 2



    Be sure to check back often, because assignments may change!
    Last modified: October 5, 1999


    Due Monday 9/27 at 9am

    A Guide to Writing in a Mathematics Class

    Appendices E, F, and G: These are background on Exponentials, Logarithms, and Trig functions. I've mentioned them in class, but I wanted to make it more formal.

    Section 2.1: Amount Functions and Rate Functions: The Idea of the Derivative

    E-mail Subject Line: Math 101 Your Name 9/27

    Reading questions:

      Look at the graphs of P(t) and V(t) on page 95
    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. Give a value of t where the second derivative of P is zero.

    Reminders:


    Due Wednesday 9/29 at 9am

    Review Guidelines for Homework Presentation

    Section 2.2: Estimating Derivatives: A Closer Look

    E-mail Subject Line: Math 101 Your Name 9/29

    Reading questions:

    1. What does the term "locally linear" mean?
    2. Explain why the derivative of f(x)=|x| does not exist at x=0.

    Reminder:


    Due Friday 10/1 at 9am

    Section 2.3: The Geometry of Derivatives

    E-mail Subject Line: Math 101 Your Name 10/1

    Reading questions:

      Look at the graph of f' in Example 2:
    1. Where does f have stationary points?
    2. Where is f increasing?
    3. Where is f concave up?

    Reminder:


    Due Monday 10/4 at 9am

    Section 2.4

    E-mail Subject Line: Math 101 Your Name 10/4

    Reading questions:

      Use the graphs of f, f', f" on page 133.
    1. By looking at the graph of f", how can you tell where f is concave up and concave down?
    2. By looking at th egraph of f', how can you tell where f is concave up and concave down?

    Note:
    The relationships exhibited in the reading questions should not be memorized. If you understand them, you can reproduce them at any time, and you're unlikely to make the silly mistakes that can happen when you memorize.

    Reminders:


    Due Wednesday 10/6 at 9am

    Section 2.5: Average and Instantaneous Rates: Defining the Derivative

    New Note: As of today, 10/5, there is a change in plans. We will not talk about this section (2.5) until Friday's class. However, I don't want to assign reading over Fall Break. So I'll assign the reading on Section 2.6 for either Friday or Wednesday, and you can do it whenever fits your schedule better.

    E-mail Subject Line: Math 101 Your Name 10/6

    Reading questions:

    1. Let f(x)=x3. Find the slope of the secant line from x=-2 to x=4.
    2. For a function f, what does the difference quotient [f(a+h)-f(a)]/h measure?
    3. Let f(x)=x3 (again). What is the average rate of change of f from x=-2 to x=4?

    Reminders:


    Due Friday 10/8 at 9am

    Notice: This reading assignment really isn't due until Wednesday the 13th. Depending on your plans for break, you may want to do it now, or you may decide to wait.

    Section 2.6

    Note:
    Read the formal definition of limit, but don't obsess over it.

    Note 2:
    There's a proof of the fact that the limit of sin(t)/t as t approaches 0 is 1 in Appendix H. (The book cites Appendix I, or at least my copy does). E-mail Subject Line: Math 101 Your Name 10/13

    Reading questions:

    1. Let g(x)=(x2-9)/(x-3) as in Example 2, section 2.6
      • Is g(x) defined at x=3? Why or why not?
      • What is lim x->3 g(x)? Why?
    2. Is n(x) in Example 8 (section 2.6) continuous at x=-3? Why or why not?


      Due Monday 10/11 at 9am

      Nothing! It's Fall Break!


      Due Wednesday 10/13 at 9am

      I hope you enjoy/enjoyed your break!
      Section 2.6:

      • To read: All
      • Be sure to understand: The connection between Examples 2 and 3; the definition of continuity on page 157.

      Note:
      Read the formal definition of limit, but don't obsess over it. But beware--you used to have to learn and grasp this!

      E-mail Subject Line: Math 101 Your Name 10/13

      Reading questions:

      1. Let g(x)=(x2-9)/(x-3) as in Example 2, section 2.6
        • Is g(x) defined at x=3? Why or why not?
        • What is lim x->3 g(x)? Why?
      2. Is n(x) in Example 8 (section 2.6) continuous at x=-3? Why or why not?

      Reminders:

      • The next problem set will be due this Friday; the only new material is 2.5, but there's some more problems from Section 2.3 and Section 2.4. Also, of course, if you didn't do the problems from Section 2.4 last week, as they weren't on the exam, this would be the time to do them!


      Due Friday 10/15 at 9am

      Section 2.7:

      • To read: Skip Examples 4,5, and 7, and skip the squeeze principle. Read the rest.
      • Be sure to understand: Examples 1 and 3; the section Finding Limits Graphically and Numerically
      • Note: We're reading this section now to avoid having to read anything over break.

      E-mail Subject Line: Math 101 Your Name 10/15

      Reading questions:

      1. Find lim x->oo 1/x3 and explain.
      2. Find limx-> 0 exp(sin(x)/x) and explain.


      Here ends Chapter 2
      Go to Chapter 3!


      Janice Sklensky
      Wheaton College
      Department of Mathematics and Computer Science
      Science Center, Room 103
      Norton, Massachusetts 02766-0930
      TEL (508) 286-3970
      FAX (508) 285-8278
      jsklensk@wheatonma.edu


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