1. If a function f has a Taylor (power) series representation around x_0, what can you say about the coefficients of that power series?

2. What is a Maclaurin series? Explain why f(x)=|x| does not have a Maclaurin series.

4. What is a Taylor polynomial? Is there any connection between a Taylor series and Taylor polynomials?

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. Explain the difference between absolute and conditional convergence. What does Theorem 10 say about the relationship between the two?

2. What does the alternating series test (AST) say ?

3. Can you conclude divergence based on AST?

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 "comparison test"? Give an intuitive explanation for why it works.

2. What is a p-series? How can you tell if a p-series converges?

3. What is the ratio test?

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) Decide if the following statements are True or False

i) If a series converges, its general term goes to 0

ii) If the terms of a series go to 0, then series converges

2) What, if any, is the difference between a "sequence" and "series"? What is the relationship between convergence of sequences and convergence of series?

3) Why are geometric series so nice? When does a geometric series converge?

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

1. What is the formal definition of a sequence?

2. Give a major difference between a function a real variable, and a sequence

3. Give at least two alternative ways (other than the formal definition) of viewing a sequence.

4. Do you think the converse of the Fact on page 550 is correct?

5. What is a monotone sequence?

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

1) In finding volumes by cross sectioning, what do we assume about cross sectional area when Delta x (thickness) is small? What is the volume of such a section, approximately?

2) What are the cross sections of solids of revolutions like?

3) What is the area of the washer? (Your answer should include the terms "inner radius" and "outer radius")

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

1. What does the word "error" mean in connection with approximating sums for integrals?

2. If a function f is decreasing over an interval, what can you say about the relationship between Rn and Ln on that interval? Why does this relationship hold?

3. If a function f is concave up over an interval, what can you say about the relationship between Tn and Mn on that interval? Why does this relationship hold?

4. The Simpson's rule can be thought of as a "weighted average" of two other sums. What are they? Which one gets more weight and why?

5. Do the error bounds for Rn and Ln depend on the first or the second derivative of the function?

6. Do the error bounds for Mn and Tn depend on the first or the second derivative of the function?

7. Was there anything specific that was confusing to you?

1. What is the purpose/use of sigma (summation) notation

2. What is the value of the sum 1+2+3+....+200? (use the appropriate formula to find it)

3. What is the value of the sum 1^2+2^2+3^2+....+50^2?

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. Which do you think is the most accurate way to approximate an integral: Left Sums, Right Sums, or Trapezoid Sums? Why?

2.Which of the following is not a Riemann sum? Left Sum, Right Sum, Midpoint Sum, Trapezoid Sum.

3. What is a regular partition? Can a Riemann sum use a partition that is not regular?

4. What is the formal definition of definite integral in terms of Riemann sums?

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. Why do we need a numerical method to solve DEs?

2. When/why do we need computers to use Euler's method?

3. What does each step of Euler method produce? How do we go from one point to the next?

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

1. What are the two important advantages of symbolic methods of solving of differential equations over numerical and graphical methods? What is the main disadvantage of symbolic methods?

2. Give an example of a separable differential equation and an example of a non-separable differential equation.

3.What is the a general approach for solving the separable DE?

4. Give some examples of applications of separable DE's.

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

1. What does the comparison theorem for improper integrals say? State it in your own words.

2. What is "the p-test" for integrals?

3. What is an absolutely convergent improper integral?

4. What does it mean to say that "convergent integrals have skinny tails?"

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

Section 4.2 (S-12) and

10.1

1. What is the method given in the book to find the limit of a rational function as x goes to infinity (or negative infinity)?

2. Briefly explain what an indeterminate form means. Give at least 3 types of indeterminate forms. There are actually more indeterminate forms than those described in the book. Do you know any additional indeterminate forms?

3. What types of indeterminate forms does the l'Hopital's rule deal with?

4. What makes an integral improper?

5. What do we do if an improper integral has more than one problem?

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

4.2: 3,4,13,14,26,36,

10.1: 1-7

1) What techniques of antidifferentiation have we learned so far?

2) How do differentiation and integration (antidifferentiation) compare? Is one more starightforward than the other?

3) Based on your practice so far and reading the section 8.4, given an integral do you have some idea of what technique to try? Do you find any of the techniques to be particularly difficult to apply? Do you feel like you need more practice or guidance?

1) Complete the following expressions to a square:

a) x^2+3x+1 b) -x^2-x (Just give the final answer, don't show intermediate steps)

2) What are the Pythagorean identities and double-angle formulas?

3) State what trig substitution is used for integrals involving each of thefollowing: a) sqrt(4-x^2) b) sqrt(x^2-3) c) sqrt(3x^2+5)

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. Why do we bother calculating antiderivatives by hand, instead of just asking Maple do it for us?

2. Integration by parts is related to which differentiation formula?

3. Which of the following functions is a good candidate for antidifferentiation by parts:

f(x) = x exp(x^2 ) or f(x) = x^2 exp(x)? Explain?

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

i) What are the 3 steps in using the method of substitution?

ii) What rule of differentiation justifies the method of substitution?

iii) How do we handle definite integral when we use substitution?

iv) Was there anything specific that was confusing to you? Is there any specific (or general) question you would like to have answered?

Notes for Students (xviii), hand outs from the first day

and

Section 5.3

o) Tell me about the best and worst math teachers you ever had. What did they do you liked/disliked so much?

i) What is the authors' answer to "Why do we study calculus"?

ii) What is different about mathematical language from natural languages?

iii) Why does FTC have such a high-sounding name?

iv) If we are given a definite integral which version of FTC do we use? Explain in words how we compute definite integrals using FTC

v) Is FTC good to solve every integration problem?

vi) Was there anything specific that was confusing to you? Is there any specific (or general) question you would like to have answered?