Reading Assignments for Calculus 2
    Spring 2006, Math 104

    January and February, 2006



    Be sure to check back often, because assignments may change!
    (Last modified: Friday, February 24, 2006, 10:04 AM )


    I'll use Maple syntax for mathematical notation on this page.
    All section and page numbers refer to sections from Ostebee/Zorn, Volume 2, 2nd edition.


    Due Friday 1/27 at 9am

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    Section 5.1: Areas and Integrals
    Section 5.2: The Area Function
    Section 5.3: The Fundamental Theorem of Calculus

    E-mail Subject Line: Math 104 Your Name 1/27

    Reading questions:

    1. Why do you think it makes sense to call
      int(f(x),x=a..b)/(b-a)
      the average value?

      Notes:

      • The above is written in Maple notation -- it's as good a way as any to write mathematical ideas without symbols, with the added benefit that it gets you used to some Maple notation. The above says the integral of f(x), from x=a to x=b, all divided by b-a.
      • The text doesn't specifically address this question; the reason I'm asking this is because this is exactly the sort of question you should be learning to ask yourself (and attempting to answer) when you read.
    2. Find the signed area between x^5 and the x-axis from x=1 to x=2.
    3. If f(x) is continuous, must it have an antiderivative? If your answer is yes, does that mean there must be a nice formula (or any formula at all) for the antiderivative?

    Reminders:

    Please Note:


    Due Monday 1/30 at 9am

    Problem Set Guidelines
    Section 3.4 Inverse Functions and Their Derivatives (Appendix S in your book, I believe)

    E-mail Subject Line: Math 104 Your Name 1/30

    Reading questions:

    1. What is the domain of the function arccos(x)? Why is this the domain?
    2. Explain how we can tell lines which are neither horizontal nor vertical have inverses.
    3. Why do you think we are studying the inverse trig functions now?
    4. Find one antiderivative of 1 / (1+x2).

    Reminder:


    Due Wednesday 2/1 at 9am

    More on Antidifferentiation & Inverse Trig Functions

    No Reading Questions Today

    Reminder:


    Due Friday 2/3 at 9am

    Section 5.4 Finding Antiderivatives; The Method of Substitution

    E-mail Subject Line: Math 104 Your Name 2/3

    Reading questions:

    1. Explain the fundamental difference between a definite integral and an indefinite integral. Please go deeper than saying one has limits of integration and one doesn't. The first is a real number -- why? what does it represent? Then think similarly about indefinite integrals.
    2. Substitution attempts to undo one of the techniques of differentiation. Which one is it?
    3. What are the three steps in the process of substitution?

    Reminder:


    Due Monday 2/6 at 9am

    Section 5.6 Approximating Sums; The Integral as a Limit

    E-mail Subject Line: Math 104 Your Name 2/6

    Reading questions:

    1. Give an example of a partition of the interval [0,3].
    2. When approximating an integral, which would you expect to be more accurate, L10 or L100? Why?
    3. Explain the idea of a Riemann sum in your own words.

    Reminders:


    Due Wednesday 2/8 at 9am

    Problem Set Guidelines
    Section 6.1 Approximating Integrals Numerically

    E-mail Subject Line: Math 104 Your Name 2/8

    Reading questions:

    1. Why would we ever want to approximate an integral?
    2. Let f(x)=x2 and I=int( f(x), x= -1. . 2). Does Theorem 1 apply to I? Explain.
    3. Let f(x)=x2 and I=int( f(x), x= -1. . 2). Does Theorem 2 apply to I? Explain.

    Reminders:


    Due Friday 2/10 at 9am

    Section 6.2 Error Bounds for Approximating Sums

    E-mail Subject Line: Math 104 Your Name 2/10

    Reading questions:

    1. Explain in words what K1 is in Theorem 3.
    2. Explain in words what K2 is in Theorem 3.
    3. Find values for K1 and K2 for int( x3, x= -3. . 1).


    Due Monday 2/13 at 9am

    Section 6.2 Error Bounds for Approximating Sums
    Section 7.1 Measurement and the Definite Integral; Arc Length

    E-mail Subject Line: Math 104 Your Name 2/13

    Reading questions:

    1. How many subdivisions does the trapezoid method require to approximate int( cos(x3), x = 0. . 1) with error less than 0.0001?

    2. Let f(x)=sin(Pi*x/2)+10 and g(x)=3x/10+10.

      (a) Set up the integral that determines the area of the region bounded by y=f(x) and y=g(x) between x=0 and x=5/3.
      (b) Set up the integral that gives the length of the curve y=g(x) from x=-1 to x=3.

    Reminders:


    Due Wednesday 2/15 at 9am

    Section 7.2 Finding Volumes by Integration

    E-mail Subject Line: Math 104 Your Name 2/15

    Reading questions:

    1. Let R be the rectangle formed by the x-axis, the y-axis, and the lines y=1 and x=3. What is the shape of the solid formed when R is rotated about the x-axis?
    2. Let T be the triangle formed by the lines y=x, x=1 and the x-axis. What is the shape of the solid formed when T is rotated about the x-axis?

    Reminder:


    Due Friday 2/17 at 9am

    Section 7.2 Finding Volumes by Integration

    Reminders:


    Due Monday 2/20 at 9am

    Bring Questions for Exam 1

    No Reading Questions Today

    Reminders: