Be sure to check back, because this may change during the semester.
All numbers indicate sections from
Calculus by Taalman and Kohn.
For Friday January 27 (Due 1/26 @ 8:00 pm)
Section 0.4 Exponential and Trigonometric Functions
To read
 Topics:
 Exponential Functions
 Logarithmic Functions
 Examples: 1a, 2a, 3ab
Reading Questions
 How are the functions f(x)=2^{x} and g(x)=log_{2}(x) related?
 Solve for x in the equation log_{2}(x) + log_{2}(x^{3})=12.
Submit answers through onCourse
For Monday January 30 (Due 1/29 @ 8:00 pm)
Section 0.4 Exponential and Trigonometric Functions
To read
 Topics:
 Examples: 1b, 2b, 3c
Reading Questions
 What is 120 degrees equal to in radians?
 What is the period of the sine function? How can you tell from the graph?
Submit answers through onCourse
For Wednesday February 1 (Due 1/31 @ 8:00 pm)
Section 2.1 An Intuitive Introduction to Derivatives
To read
 Topics:
 Slope Functions
 Position and Velocity
 Approximating the Slope of a Tangent Line
 Examples: 1, 2, 3
Reading Questions
 Look at the leftmost graph on page 156. Is the function f positive or negative at x=0? How about the derivative of f at x=0? Explain.
 Let f(x)=x^{2}. Find the slope of the secant line connecting the points
(1,1) and (3,9) on the graph y=f(x).
Submit answers through onCourse
For Friday February 3 (Due 2/2 @ 8:00 pm)
Section 1.1 An Intuitive Introduction to Limits
To read
 Topics:
 Examples of Limits
 Limits of Functions
 Infinite Limits, Limits at Infinity, and Asymptotes

 Examples: 1, 2, 3
Reading Questions
 Why do you think we're studying limits now?
 If f(x)=x^{2}, what is lim_{x→2}f(x)? Explain.
 If f(x)=1/x, what is lim_{x→0}f(x)? Explain.
Submit answers through onCourse
For Monday February 6 (Due 2/5 @ 8:00 pm)
Section 1.4 Continuity and Its Consequences
To read
 Topics:
 Defining Continuity with Limits
 Types of Discontinuities
 Continuity of Very Basic Functions
 Extreme and Intermediate Values of Continuous Functions
 Examples: 1, 3, 5
Reading Questions
 How can you tell from the graph of y=f(x) if the function f(x) is continuous?
 Give an example of a function that is discontinuous at x = 3.
 Give an intuitive explanation for why the Intermediate Value Theorem is true.
Submit answers through onCourse
For Wednesday February 8 (Due 2/7 @ 8:00 pm)
Section 1.6 Infinite Limits and Indeterminate Forms
To read
 Topics:
 Infinite Limits
 Limits at Infinity
 Indeterminate and NonIndeterminate Forms
 Examples: 1, 2ab, 3
Reading Questions
 Give an example of a function that has a vertical asymptote at x = 3.
 Give an example of a function that has a horizontal asymptote at y = 3.
Submit answers through onCourse
For Friday February 10 (Due 2/9 @ 8:00 pm)
Section 2.2 Formal Definition of the Derivative
To read
 Topics:
 The Derivative at a Point
 The Derivative as a Function
 Differntiability
 Tangent Lines at Local Linearity
 Examples: 1  4
Reading Questions
 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)
 What is an advantage of determining f '(x), the derivative function, rather than f '(a), the derivative at a specific point x=a?
Submit answers through onCourse
For Monday February 13 (Due 2/12 @ 8:00 pm)
Section 2.3 Rules for Calculating Basic Derivatives
To read
 Topics:
 Derivatives of Linear Functions
 The Power Rule
 The Constant Multiple and Sum Rules
 The Product and Quotient Rules
 Examples: 1, 2, 4
Reading Questions
 If f(x)=x^{8}, what is f '(x)?
 If f(x)=x^{1/3} (the cube root of x), use the graph of y=f(x) to explain why f '(0) does not exist.
 Explain what is wrong with the following calculation and fix it:
f(x)= (x^{2} + 7x) (x^{3}  5x +9)
f '(x)=(2x+7)(3x^{2}5)
Submit answers through onCourse
For Wednesday February 15
Reread Section 2.3 Rules for Calculating Basic Derivatives
No Reading Questions for today.
For Friday February 17 (Due 2/16 @ 8:00 pm)
Section 2.4 The Chain Rule and Implicit Differentiation
To read
 Topics:
 Differentiating Compositions of Functions
 Examples: 1, 2
Reading Questions
Explain what is wrong with the following calculations and fix them.

f(x)= (x^{2}+2x)^{130}
f '(x)=130(x^{2}+2x)^{129}

f(x)= (x^{3}+8x^2)^{12}
f '(x)=12(3x^{2}+16x)^{11}
Submit answers through onCourse
For Monday February 20
Q&A for Exam 1. No Reading Assignment.
For Wednesday February 22
Section 2.5 Derivatives of Exponential and Logarithmic Functions
To read
 Topics:
 Derivatives of Exponential Functions
 Exponential Functions Grow Proportionally to Themselves
 Derivatives of Logarithmic Functions

 Examples: 1, 3
Reading Questions
 What is the 42nd derivative of f(x)=e^{x}?
 If g(x)=x ln(x)  x, find g'(x).
Submit answers through onCourse
For Friday February 24 (Due 2/23 @ 8:00 pm)
Section 2.6 Derivatives of Trigonometric and Hyperbolic Functions
To read
 Topics:
 Derivatives of Trigonometric Functions
 Examples: 1
Reading Questions
 What is the value of lim_{θ > 0} sin(θ) / θ ? (Hint: Look at the graph)
 What is the value of lim_{θ > 0} (1cos(θ)) / θ ? (Hint: Look at the graph)
 Why do we care about these limits?
Submit answers through onCourse
For Monday February 27 (Due 2/26 @ 8:00 pm)
Reread Section 2.6 Derivatives of Trigonometric and Hyperbolic Functions
No Reading Questions for today.
For Wednesday March 1 (Due 2/28 @ 8:00 pm)
Section 3.1 The Mean Value Theorem
To read
 Topics:
 The Derivative at a Local Extremum
 The Mean Value Theorem
 Examples: 1, 4, 5
Reading Questions
 If f(x)= 3x^{2}  6x, is x=1 a critical value? Why or why not? How about x=0?
 Explain the Mean Value Theorem using "car talk" (that is, in terms of velocity).
Submit answers through onCourse
For Friday March 3
Differentiation Exam. No Reading Assignment.
For Monday March 6 (Due 3/5 @ 8:00 pm)
Section 3.2 The First Derivative and Curve Sketching
To read
 Topics:
 Derivatives and Increasing/Decreasing Functions
 Functions with the Same Derivative
 The First Derivative Test
 Examples: 1, 2, 3
Reading Questions:
Let f(x) = x^{4}  4 x^{3} + 2
 Show that f has critical points at x=0 and x=3.
 Use the First Derivative Test to classify the critical point at
x=3 as a local maximum, a local minimum, or neither.
 Use the First Derivative Test to classify the critical point at
x=0 as a local maximum, a local minimum, or neither.
Submit answers through onCourse
For Wednesday March 8 (Due 2/28 @ 8:00 pm)
Section 3.3 The Second Derivative and Curve Sketching
To read
 Topics:
 Derivatives and Concavity
 Inflection Points
 The SecondDerivative Test
 CurveSketching Strategies
 Examples: 1, 2, 3
Reading Questions:
Let f(x) = x^{4}  6 x^{2} + 8x + 2
 Show that f has critical points at x=2 and x=1.
 Use the Second Derivative Test to classify the critical point at
x=2 as a local maximum, a local minimum, or neither.
 Use the First Derivative Test to classify the critical point at
x=1 as a local maximum, a local minimum, or neither.
Submit answers through onCourse
For Friday March 10
Flex Day. No Reading Assignment.
March 13  17
Spring Break. Surprisingly, no Reading Assignments.
For Monday March 20 (Due 3/19 @ 8:00 pm)
Section 3.4 Optimization
To read
 Topics:
 Finding Global Extrema
 Translating Word Problems into Mathematical Problems
 Examples: 1, 2
Reading Questions
Let f(x) = x^{4}  6 x^{2} + 8x + 2
 On the interval [3,2], at which xvalues can the global maximum and global minimum of f(x) occur?
 What is the global minimum of f(x) on the interval [3,2]? What is its global maximum on this interval?
Submit answers through onCourse
For Wednesday March 22
Reread Section 3.4 Optimization, including Examples 3 & 4.
No Reading Questions for today.
For Friday March 24
Reread Section 3.4 Optimization, including Examples 3 & 4.
No Reading Questions for today.
For Monday March 27
Q&A for Exam 2. No Reading Assignment.
For Wednesday March 29
No Reading Assignment for today
For Friday March 31
No Reading Assignment for today
For Monday April 3 (Due 4/2 @ 8:00 pm)
Section 4.1 Addition and Accumulation
To read
 Topics:
 Accumulation Functions
 Sigma Notation
 The Algebra of Sums in Sigma Notation
 Examples: 1, 2, 3
Reading Questions
 Calculate Σ^{5}_{k=1} 3k^{2}
 Why do you think we are introducing sigma notation now?
Submit answers through onCourse
For Wednesday April 5 (Due 4/4 @ 8:00 pm)
Section 4.2 Riemann Sums
To read
 Topics:
 Subdivide, Approximate, and Add Up
 Approximating Area with Rectangles
 Riemann Sums
 Types of Riemann Sums
 Examples: 1, 2, 4
Reading Questions
 What is the purpose of a Riemann sum?
 If f(x)=x^{2}, will a right sum for f on [0,2] underestimate or overestimate the area under the curve? Why?
Submit answers through onCourse
For Friday April 7
Reread Section 4.2 Riemann Sums.
No Reading Questions for today.
For Monday April 10 (Due 4/9 @ 8:00 pm)
Section 4.3 Definite Integrals
To read
 Topics:
 Defining the Area Under a Curve
 Properties of Definite Integrals
 Examples: 1, 4, 5
Reading Questions
 Find ∫_{0}^{1} 2x dx
 Will the definite integral ∫_{0}^{2} x5 dx be positive or negative? Why?
Submit answers through onCourse
For Wednesday April 12 (Due 4/11 @ 8:00 pm)
Section 4.4 Indefinite Integrals
To read
 Topics:
 Antiderivatives and Indefinite Integrals
 Antidifferentiation Formulas
 Antidifferentiating Combinations of Functions
 Examples: 1, 2, 3, 4
Reading Questions
 What is the difference between a definite integral and an indefinite integral?
 Find ∫ 2x + cos(x) dx
Submit answers through onCourse
For Friday April 14
Flex Day. No Reading Assignment.
For Monday April 17 (Due 4/16 @ 8:00 pm)
Section 4.5 The Fundamental Theorem of Calculus
To read
 Topics:
 The Fundamental Theorem
 Using the Fundamental Theorem of Calculus
 Examples:1, 2, 3
Reading Questions
 Find the area of the region above the xaxis and below the graph of f(x)= 4/x + cos(x) + 1 between x=1 and x=10.
 Does it matter which antiderivative F you pick to use in the Fundamental Theorem? Explain.
Submit answers through onCourse
For Wednesday April 19 (Due 4/18 @ 8:00 pm)
Section 4.7 Functions Defined by Integrals
To read
 Topics:
 Area Accumulation Functions
 The Second Fundamental Theorem of Calculus
 Examples:1, 2, 3
Reading Question
Does every continuous function have an antiderivative? Why or why not?
Submit answers through onCourse
For Friday April 21
Flex Day. No Reading Assignment.
For Monday April 24
Section 5.1 Integration by Substitution
To read
 Topics:
 The Art of Integration
 Undoing the Chain Rule
 Choosing a Useful Substitution
 Finding Definite Integrals by Using Substitution
 Examples: 1, 2, 3, 5
Reading Questions
 Substitution attempts to undo one of the techniques of differentiation. Which one is it?
 Use usubstitution to find an antiderivative of f(x) = 3x^{2} cos(x^{3})
 Explain why ∫ cos(x) sin(x)^{2} dx and ∫ ln(x)^{2} / x dx are essentially the same integral after performing a substitution.
Submit answers through onCourse
For Wednesday April 26 (Due 4/25 @ 8:00 pm)
Reread 5.1 Integration by Substitution
No Reading Questions for today.
For Friday April 28
Flex Day. No Reading Assignment.
For Monday May 1
Q&A for Exam 3. No Reading Assignment.
For Wednesday May 3
The BIG Picture. No Reading Assignment.
For Friday May 5
The BIG Picture. No Reading Assignment.
