For 2 October

• To read: Through page 146. Be warnded: This is a hard section!
• Be sure to understand: Example 1, the Section on page 143 Average Speeds, Instantaneous Speeds, and Limits
• Possible Reading Quiz questions:
  
  1. For a function f, what does the difference quotient ( f(a+h) - f(a) )/ h measure?
  2. Let f(x)=x^2. What is the average rate of change of f from x=1 to x=3?
  3. Let f(x)=x^2. What is the slope of the secant line connecting the points (1,1) and (3,9) on the graph of y=f(x)?

For 4 October

• 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
• Possible Reading Quiz questions:
  Let g(x)=(x^2 - 9)/(x-3) as in Example 2.
  1. Is g(x) defined at x=3? Why or why not?
  2. What does lim_(x->3) g(x) equal?
  3. Is g(x) continuous at x=3? Why or why not?

For 7 October

• 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
• Possible Reading Quiz questions:
  Find the following limits:
  1. lim_(x->infinity) 1/x^3
  2. lim_(x->0^+) 1/x^3
  3. lim_(x->infinity) cos(x)

For 9 October

• 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
• Possible Reading Quiz questions:
  
  1. What does it mean for the function F to be an antiderivative of the function f?
  2. Let f(x)=x^2. What is f'(x)?
  3. Let f(x)=x^2. Find an antiderivative of f(x).

For 11 October

• 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
• Possible Reading Quiz questions:
  
  1. If f is a differentiable function defined on an interval I, at which x-values can the maximum and minimum values of f on I occur?
  2. 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 16 October

• 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
• Possible Reading Quiz questions:
  No reading quiz today, but you should be able to answer:
  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 18 October

• 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
• Possible Reading Quiz 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 21 October

• To read: All
• Be sure to understand: Theorems 9 and 10, and Exhibit B, pg 219
• Possible Reading Quiz questions:
  Find 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 28 October

• To read: All
• Be sure to understand: Theorem 11 and Example 3
• Possible Reading Quiz 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 30 October

• To read: All. This section will require some extra work.
• Be sure to understand: Examples 3 and 6.
• Possible Reading Quiz questions:
  No quiz today because of the Differentiation Exam, but you should be able to do Exercises 1, 3, 4 on page 254.

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