Reading Assignments for Calculus 1
    Spring 2001, Math 101

    March 2001



    Be sure to check back often, because assignments may change!
    Last modified: 3/21/01


    I'll use Maple syntax for mathematical notation on this page.
    All section and page numbers refer to sections from Ostebee/Zorn, Vol 1.


    Due Friday 3/2 at 8am

    Section 2.5 : Average and Instantaneous Rates: Defining the Derivative

    E-mail Subject Line: Math 101 Your Name 3/2

    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 Monday 3/5 at 8am

    Section 2.5 : Average and Instantaneous Rates: Defining the Derivative
    Guide to Writing Mathematics

    E-mail Subject Line: Math 101 Your Name 3/5

    Reading questions:

      Let f(x) = x3 (as we did on Friday).
    1. Find the slope of the secant line from x= 1 to x=3.
    2. Find the slope of the secant line from x=1.9 to x=2.1.
    3. Which of these do you think is closer to the slope of the tangent line at x=2?
    4. What is the average rate of change of f for x between x=1 and x=3? What is the average rate of change of f for x between x=1.9 to x=2.1? Which of these do you think is closer to the rate f is changing when x=2?
    5. What does the quotient [f(x)-f(a)]/[x-a] represent?

    Reminders:


    Due Wednesday 3/7 at 8am

    Section 2.6: Limits and Continuity

    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 3/7

    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?

    Reminder:


    Due Friday 3/9 at 8am

    Section 2.7 : Limits Involving Infinity: New Limits from Old

    E-mail Subject Line: Math 101 Your Name 3/9

    Reading questions:

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

    Reminder:


    Monday 3/12 through Friday 3/16: Spring Break


    Due Monday 3/19 at 8am

    Section 3.1: Derivatives of Power Functions and Polynomials
    Section 3.2: Using Derivatives and Antiderivative Formulas

    E-mail Subject Line: Math 101 Your Name 3/19

    Reading questions:

    1. Let f(x)=x10. What is f ' (x)?
    2. What does it mean for the function F to be an antiderivative of f?

    Reminder:


    Due Wednesday 3/21 at 8am

    Section 3.3: Derivatives of Exponential and Logarithmic Functions

    E-mail Subject Line: Math 101 Your Name 3/21

    Reading questions:

    1. Find an antiderivative for f(x)=ex.
    2. What is the derivative of g(x)=ln(x)?
    3. What is slope of the line tangent to y=ex at the point (0,1)?

    Reminders:


    Due Friday 3/23 at 8am

    Section 3.4: Derivatives of Trigonometric Functions

    E-mail Subject Line: Math 101 Your Name 3/23

    Reading questions:

    1. What is limh->0[ (cos(h)-1)/h]?
    2. What is limh->0[sin(h)/h]?
    3. Let f(x)=sin(x)+cos(x). What is f ' (x)?

    Reminders:


    Due Monday 3/26 at 8am

    Question and Answer for Exam 2

    No reading assignment due today!

    Reminder:


    Due Wednesday 3/28 at 8am

    Section 3.5: New Derivatives from Old: The Product and Quotient Rules

    E-mail Subject Line: Math 101 Your Name 3/28

    Reading questions:

      Find the derivatives of the following functions. Be sure to justify your answer.
    1. f(x)=xsin(x)
    2. g(x)=x/sin(x)
    3. h(x)=xln(x)-x

    Reminders:


    Due Friday 3/30 at 8am

    Section 3.6: New Derivatives from Old: The Chain Rule

    E-mail Subject Line: Math 101 Your Name 3/30

    Reading questions:

      Find the derivatives of the following functions. Be sure to justify your answer.
    1. f(x)=sin(x3)
    2. g(x)=(sin(x))3
    3. h(x)=e2x

    Reminders:


    Here ends the reading for March
    Go to the reading assignments for April!


    Janice Sklensky
    Wheaton College
    Department of Mathematics and Computer Science
    Science Center, Room 109
    Norton, Massachusetts 02766-0930
    TEL (508) 286-3973
    FAX (508) 285-8278
    jsklensk@wheatonma.edu


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