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Reading Assignments - Math 101 Calculus I - Spring 2012

Be sure to check back, because this may change during the semester.

All numbers indicate sections from Multivariable Calculus, Early Transcendental Functions 3e by Smith and Minton.

For Friday January 27

Section 0.1 Polynomials and Rational Functions
Section 0.4 Trigonometric Functions

To read: All of Section 0.1, through Example 4.4 in Section 0.4

Reading Questions:

  1. Give the equation of the line through the point (1,2) that is parallel to the line y=4x+7.
  2. What is 120 degrees equal to in radians?
  3. What is the period of the cosine function? How can you tell from the graph?

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For Monday January 30

Section 0.5 Exponential and Logarithmic Functions

To read: Through Example 5.10

Reading Questions:

  1. How are the functions f(x)=2x and g(x)=log2(x) related?
  2. Solve for x in the equation log2(x) + log2(x3)=12.

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For Wednesday February 1

Section 0.6 Transformations of Functions

To read: All

Reading Questions: Let f(x)=x2.

  1. What is f(7)? What is f(x-1)?
  2. How is the graph of y=f(x)+3 = x2+3 related to the graph of y=f(x)?
  3. How is the graph of y=f(x+3) = (x+3)2 related to the graph of y=f(x)?

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For Friday February 3

Section 1.1 A Brief Preview of Calculus
Section 1.2 The Concept of Limit

To read: All

Reading Questions:

  1. Let f(x)=x2. Find the slope of the secant line connecting the points (1,1) and (3,9) on the graph y=f(x).
  2. Evaluate lim x -> 3 (x2-9) / (x-3)
  3. What is the connection between Questions 1 and 2?

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For Monday February 6

Section 1.4 Continuity and its Consequences

To read: All

Reading Questions:

  1. How can you tell from the graph of y=f(x) if the function f(x) is continuous?
  2. Give an example of a function that is discontinuous at x=3.
  3. Give an intuitive explanation for why the Intermediate Value Theorem is true.

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For Wednesday February 8

Section 1.5 Limits Involving Infinity; Asymptotes

To read: Through Example 5.7

Reading Questions:

  1. Give an example of a function that has a vertical asymptote at x=3.
  2. Give an example of a function that has a horizontal asymptote at y=-1.

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For Friday February 10

Section 2.1 Tangent Lines and Velocity

To read: All

Reading Questions:

  1. Give an intuitive geometric explanation for the definition of the slope of a tangent line (Definition 1.1).
  2. What is the difference between speed and velocity?

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For Monday February 13

Section 2.2 The Derivative

To read: All

Reading Questions:

  1. If f(x) is a function, give two different interpretations of the value f'(a), the derivative of f at x=a. (Hint: Think about Section 2.1)
  2. What is an advantage of determining f'(x), the derivative function, rather than f'(a), the derivative at a specific point x=a?

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For Wednesday February 15

Section 2.3 Computation of Derivatives: The Power Rule

To read: All

Reading Questions:

  1. If f(x)=x3, what is f'(x)?
  2. If f(x)=x1/3 (the cube root of x), use the graph of y=f(x) to explain why f'(0) does not exist.

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For Friday February 17

Section 2.4 The Product and Quotient Rules

To read: All

Reading Questions: Explain what is wrong with the following calculations and fix them.

  1. f(x)= (x2 + 7x) (x3 - 5x +9)
    f'(x)=(2x+7)(3x2-5)

  2. g(x) = (x2+3) / (x7-4x)
    g'(x)= (2x) / (7x6-4)

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For Monday February 20

Q&A for Exam 1. No Reading Questions for today.

For Wednesday February 22

Section 2.5 The Chain Rule

To read: All

Reading Questions: Explain what is wrong with the following calculations and fix them.

  1. f(x)= (x2+2x)130
    f'(x)=130(x2+2x)129

  2. f(x)= (x3+8x^2)12
    f'(x)=12(3x2+16x)11

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For Friday February 24

Section 2.6 Derivatives of the Trigonometric Functions

To read: All

Reading Questions:

  1. What is the value of limθ -> 0 sin(θ) / θ ?
  2. What is the value of limθ -> 0 (1-cos(θ)) / θ ?
  3. Why do we care about these limits?

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For Monday February 27

Section 2.7 Derivatives of the Exponential and Logarithmic Functions

To read: Through Example 2.12

Reading Questions:

  1. What is the 42nd derivative of f(x)=ex?
  2. If g(x)=x ln(x) - x, find g'(x).

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For Wednesday February 29

No Reading Assignment for today, but review Sections 2.3 - 2.7.

For Friday March 2

Flex day on the schedule. No Reading Assignment.

For Monday March 5

Section 2.9 The Mean Value Theorem

To read: All

Reading Questions:

  1. What are the hypotheses of the Mean Value Theorem?
  2. What is the conclusion of the Mean Value Theorem?
  3. Explain the MVT using "car talk" (that is, using velocity).

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For Wednesday March 7

Section 3.1 Linear Approximations

To read: Through Example 1.2

Reading Questions:

  1. Why would you want to use a linear approximation?
  2. Use the linear approximation of sin(x) at x0=0 to approximate sin(π/17).

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For Friday March 9

No Reading Assignment for today.

For March 12 - 16

Spring Break!

For Monday March 19

3.3 Maximum and Minimum Values

To read: All. Pay special attention to the statements of Theorems 3.1, 3.2, and 3.3.

Reading Questions:

  1. If f(x)= 3x2 - 6x, is x=1 a critical value? Why or why not? How about x=0?
  2. At which x-values can a continuous function f(x) achieve its maximum or minimum value on a closed interval [a,b]?

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For Wednesday March 21

Section 3.4 Increasing and Decreasing Functions

To read: All

Reading Questions:

Let f(x) = x4 - 4 x3 + 2

  1. Show that f has critical points at x=0 and x=3.
  2. Use the First Derivative Test to classify the critical point at x=3 as a local maximum, a local minimum, or neither.
  3. Use the First Derivative Test to classify the critical point at x=0 as a local maximum, a local minimum, or neither.

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For Friday March 23

Section 3.5 Concavity and the Second Derivative Test

To read: All

Reading Questions:

Let f(x) = x4 - 6 x2 + 8x + 2

  1. Show that f has critical points at x=-2 and x=1.
  2. Use the Second Derivative Test to classify the critical point at x=-2 as a local maximum, a local minimum, or neither.
  3. Use the First Derivative Test to classify the critical point at x=1 as a local maximum, a local minimum, or neither.

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For Monday March 26

Section 3.7 Optimization

To read: Through Example 7.3

No Reading Questions for today

For Wednesday March 28

Section 3.7 Optimization

To read: Finish the section

For Friday March 30

Section 3.7 Optimization

Reread the section, but no Reading Questions for today

For Monday April 2

Q&A for Exam 2. No Reading Questions for today.

For Wednesday April 4

Section 4.1 Antiderivatives

To read: All

Reading Questions:

Evaluate the following indefinite integrals

  1. ∫ x2 dx
  2. ∫ x-2 dx
  3. ∫ x-1 dx

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For Friday April 6

Section 4.2 Sums and Sigma Notation

To read: Through Example 2.3

Reading Questions:

  1. Why do you think we are introducing sigma notation now?
  2. Calculate ∑i=15 (i-2)
  3. Write 1 + 23 +33 + . . . + 203 in sigma notation. You do not need to calculate this sum.

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For Monday April 9

Section 4.3 Area

To read: All

Reading Questions:

  1. Explain the idea of a Riemann sum in your own words.
  2. Give an example of a partition of [0,4].

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For Wednesday April 11

Section 4.4 The Definite Integral

To read: Through Theorem 4.3

Reading Questions:

  1. Will the definite integral ∫02 x2 - 2x dx be positive or negative? Why?
  2. What is the difference between a definite integral and an indefinite integral?

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For Friday April 13

Section 4.5 The Fundamental Theorem of Calculus

To read: All

Reading Questions:

  1. Find the area of the region above the x-axis and below the graph of f(x)= 4/x + cos(x) between x=1 and x=2.
  2. Does every continuous function have an antiderivative? Why or why not?

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For Monday April 16

Section 4.5 The Fundamental Theorem of Calculus

Reread the section, but no Reading Questions for today

For Wednesday April 18

Section 4.6 Integration by Substitution

To read: All

Reading Questions:

  1. Substitution attempts to undo one of the techniques of differentiation. Which one is it?
  2. Give one antiderivative of (3x2) / (1 + x3 )

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For Friday April 20

Section 4.6 Integration by Substitution

Reread the section, but no Reading Questions for today

For Monday April 23

Flex day on the schedule. No Reading Assignment.

For Wednesday April 25

Section 7.1 Modeling with Differential Equations

To read: All

Reading Questions:

  1. What distinguishes a differential equation from the equations we have dealt with so far this semester?
  2. Show that y = 100 e3t is a solution to the differential equation y' = 3y.

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For Friday April 27

Section 7.1 Modeling with Differential Equations

Reread the section, but no Reading Questions for today

For Monday April 30

Q&A for Exam 3. No Reading Questions for today.

For Wednesday May 2

Flex day on the schedule. No Reading Assignment.

For Friday May 4

The BIG PICTURE for the semester. No Reading Assignment.

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