1. What are two important theorems for which continuity of functions are important hypothesis?

2. How do we use the IVT to narrow down an interval on which a continuous function must have a root?

3. What is the purpose of Newton's method?

4. Describe newton's method in your own words.

5. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1.State the first version of FTC informally

2. State the second version of FTC. Using this version, how does one compute definite integrals?

3. Why is FTC so fundamental?

4. When can we not use FTC to compute integrals?

5. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. How is the area function A_f associated with a function f defined? Describe it in words.

2. List 4 properties of the area function A_f

3. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What is the area problem?

2.What does the integral of f from a to b represent or denote?

3.What is the value of the integral of sinx from -1 to 1, and why?

4.Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What is an objective function in an optimization problem?

2. What do we try to do with the objective function?

3. If we are trying to find the dimensions of a soda can so that it can hold certain amount of soda and we use minimum amount of material, what are the objective and constraint functions?

4. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What is the general strategy for solving related rates problems?

2. Why do textbook authors love relaated rates problems?

3. How does officer Ingkvist justify his citation at the court?

4. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. When do we use implicit differentiation?

2. What is the price that we have to pay for the convenience of implicit differentiation?

3. Use implicit differentiation to find y' from the equation y^2 = x*sin(y)

4. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. Chain rule is used to differentiate what kinds of functions?

2. Find the derivative of sin(x^3)

3. Find the derivative of (sin(x^3))^3

4. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What is the derivative of x*sin(x)? What rule do you use to differentiate this?

2. What rule do we use to find derivatives of other trig functions?

3. What is an antiderivative of the function ln(x)?

4.Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What are the derivatives and antiderivatives of sin(x) and cos(x)?

2. What is the addition formula for sines?

3. The functions sin(x) and cos(x) are solutions to what differential equation? What does that DE describe physically?

4.Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What is a differential equation (DE)?

2. What is a solution to a DE ?

3. Write down a DE that expresses the following situation: The rate of change of y is proportional to itself.

4. What is an antiderivative of a given function f (see section 2.4)

5. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. Study the second proof of limit of sin(t)/t as t goes to 0 on page A-59. Is there any step you do not understand?

2. Study the formal definition of limit on page 156 and 157. State the formal definition in your own words.

3.What are the candidate points for a function to attain its maximum and minimum values over an interval.

1. What is the relationship between one sided limits (left-hand limit and right-hand limit) and the regular limit?

2.What does it mean to say "f is continuous at x =a", give the formal definition, and informal description

3. Give an informal description of the "squeeze theorem".

4. What is an "indeterminate form"? Give at least 3 types of indeterminate forms.

5. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What are the derivatives of f(x+a), f(x)+a, af(x), f(ax) in terms of derivative of f, where a is a constant?

2. Explain geometrically why (f(x)+a)' = f '(x)

3. Explain geometrically why (af(x))' = af '(x)

4. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. For h>0, what does the difference quotient (f(a+h)-f(a))/h measure or represent? State it in two way: geometrically and as a rate of change?

2. How do we obtain the derivative f '(a) from the difference quotient above?

3. When do we say that "f is differentiable at a" ?

4. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What is the relationship between concavity of a function and its second derivative?

2. Whenn f ''(a)=0, does f always have an inflection point?

3. If a is a stationary point of f and f is concave up at x=a then what do we know about point a?

4. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What is a stationary point? Define it graphically and algebraically.

2. What is an inflection point?

3. What information does the sign of f ' give about f?

4. What is the first derivative test?

5. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. What does it mean to say that a " function is locally linear"

2. Give an example of a function that is not locally linear.

3. Which function has the property that its derivative is equal to itself at every point?

4. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?

1. How is derivative defined as rate?

2. How is derivative defined graphically?

3.How is the velocity of a moving object related to its position? Is derivative involved in this relationship?

4. State the "speed limit law" formally (in terms of the speed of a car) and informally (involving f ' )

1. Give an example of a polynomial, and a non-example

2. What is a rational function?

3. What is the relationship between exponential and logarithmic functions?

4. What is the most fundamental trig identity?

How to use this book: Notes for students,

handouts for class

and Section 1.2

1. What are the rules for submitting homework in this class?

2. What is the authors' answer to "why study calculus at all"?

3. Give an example of an equation that does not define a function.

4. How is the graph of y = f(x+a) related to the graph of y = f(x) ?

5. What symmetry properties do the graphs of even and odd functions possess?

6. Was there a specific section that was confusing to you? Is there any specific (or general) question you would like to have answered?