Reading Assignments - Math 101 - Calculus I
March 1997

Be sure to check back often, because the assignments may change.
Last Modified: March 17, 1997

For March 3

Section 2.6 Limits and Continuity
  • To read: All, but you may skip the formal definition of the limit on page 155.
  • Be sure to understand: The connection between Examples 2 and 3; the definition of continuity on page 157
  • Reading Questions::
    1. Let g(x)=(x^2 - 9)/(x-3) as in Example 2.
      • 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 continuous at x= -3? Why or why not?

For March 5

Section 2.7 Limits Involving Infinity; New Limits from Old
  • To read: All, but you may skip Examples 4, 5, 7
  • Be sure to understand: Examples 1 and 3; the Squeeze Principle; the section Finding Limis Graphically and Numerically
  • Reading Questions::
    Find the following limits: Explain your answers.
    1. lim_(x->infinity) 1/x^3
    2. lim_(x->0^+) 1/x^3
    3. lim_(x->infinity) cos(x)

For March 7

Section 3.1 Derivatives of Power Functions and Polynomials
  • To read: All except for the Optional Section on pages 190-191
  • Be sure to understand: Examples 1 and 2; Theorems 1, 2, and 3; the definition of an antiderivative
Section 3.2 Using Derivative and Antiderivative Formulas
  • To read: All, plus Example 4 from Section 2.1
  • Be sure to understand: The sections Modeling Motion: Acceleration, Velocity, and Positions and Maximum-Minimum Problems and the Derivative
  • Reading Questions::
    1. Let f(x)=x^2. What is f'(x)?
    2. What does it mean for the function F to be an antiderivative of the function f?
    3. The equation h(t)=-16t^2 + v_0 t + h_0 gives the height of a falling object at time t. What do the constants v_0 and h_0 measure?

For March 10

Section 3.3 Derivatives of Exponential and Logarithm Functions
  • To read: All, but you may skip the section on Calculating the Derivative of b^x. We'll discuss this in class.
  • Be sure to understand: Theorems 5, 6, and 7
  • Reading Questions::
    1. Find an antiderivative for f(x)=e^x.
    2. What is the derivative of g(x)=ln(x).
    3. What is so special about the number e? (Hint: What is the relationship between e^a and the slope of the line tangent to y=e^x at x=a?)

For March 12

Exam today. No reading assignment.

For March 14

Section 3.4 Derivatives of Trigonometric Functions
  • To read: All, but you may skim the subsection "Differentiating the Sine Function" (we'll talk about this in more detail in class) and you may skip page 213.
  • Be sure to understand: Examples 1 and 2
  • Reading Questions::
    1. What is lim_(h->0) ( cos(h) - 1) / h?
    2. What is lim_(h->0) sin(h) / h?
    3. Let f(x)=sin(x) + cos(x). What is f'(x)?

For March 24

Section 3.5 New Derivatives from Old: The Product and Quotient Rules
  • To read: All
  • Be sure to understand: Theorems 9 and 10, and Exhibit B, pg 219
  • Reading Questions:
    Since this is the first day back from spring break, you don't have to send these in, but you should think about finding the derivatives of the following functions:
    1. f(x) = x sin(x)
    2. g(x) = x / sin(x)
    3. h(x) = x ln(x) - x

For March 26

Section 3.6 New Derivatives from Old: The Chain Rule
  • To read: All
  • Be sure to understand: Theorem 11 and Example 3
  • Reading Questions:
    Find the derivatives of the following functions:
    1. f(x) = sin(x^3)
    2. g(x) = ( sin(x) )^3
    3. h(x) = e^(2x)

For March 28

No new questions for today, but reread Section 3.6 and work on the homework.

For March 31

Section 3.7 Implicit Differentiation
  • To read: All
  • Be sure to understand: The distinction between "y is explicitly defined as a function of x" and "y is implicitly defined as a function of x"; Example 2
  • Reading Questions:
    1. Does the equation x^2 + y^2 =1 implicitly define y as one function of x? As several functions of x?
    2. Let x=y^3. Find dy/dx by implicit differentiation.

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