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Give brief but clear answers to the questions below. Click on this link to send me an email with your answers. Make sure to type 'Calculus Assignment' and the date in the subject line.

For Thursday, February 2

1. How does the determination of volumes lend itself to integration in a manner similar to the determination of areas? (In computing areas, we multiplied heights by infinitely small widths. Here, what are we multiplying by the widths?)
2. What is a washer? When are they used in computing volumes instead of solid disks? (Try and come up with a one or two sentence answer to the second question)
3. How is the side length s of the cross section of the pyramid in example 8 (page 451) determined?

For Friday, February 3

1. Give an explanation of the dimensions of the arbitrary cylindrical shell shown on page 456. (An explanation in your own words will help with both visualization of the object and understanding of settin up this type of problem.)
2. Why might Example 4 (page 458) be difficult to compute using disks/washers?
3. There is an exam in a week!!!! What would be most helpful for you in preparation for the test?

You may download a copy of the practice exam here. We will go over this on Thursday.

For Tuesday February 7

1. What would you need to determine in order to find the volume of an arbitrary cone as a volume problem? What techniques from class would be relevant in solving this problem?
2. What if the cone were made of metal and the parts were not the same throughout? (ie, if it were heavier at the top than at the bottom). If we had a function to tell us how much each part weighed, how could we determine the mass of the cone?

For Thursday, February 9

1. What concepts do you feel most comfortable with going into Friday's test?
2. What concepts might you still need to work on? Solutions to the practice exam will be posted here after class on Thursday.

For Friday, February 10

1. Relax! See me (early) if you have any questions.
2. Get a good night's sleep.
3. Arrive awake and in good physical condition (fed, caffeinated, or both, if those will help) to do your best on the exam. :)

For Tuesday, February 14

1. Familiarize yourself with formulas 1 and 2 on page 476. How do they come about as a consequence of the product rule?
2. What similarities are there between Examples 2 and 5 from section 7.1?
3. Comment: The test was easier/about as hard/harder than I expected it would be.

For Thursday, February 16

1. Review your trigonometric identities from Calculus 1 (See Appendix D if you need further assistance). Which is the most important of the trigonometric identities, from which most others are derived?
2. Answer the question above Figure 1 on page 483.
3. Formula 1 on page 486 has a very slick verification in the explanation that follows. Read through it. What other algebraic technique does this remind you of?

For Friday, February 17

1. Explain the term 'inverse substitution'. Why is it applicable to this section?
2. Review the identities used to determine the table on page 490. From what basic identity do they all emerge?
3. How would example 2 on page 491 change if we were asked to find the area of a circle?

For Tuesday, February 21

1. Breaking an integrand into partial fractions 'undoes' what third-grade technique for adding fractions?
2. What are the conditions on the degrees of the polynomials in the numerator and denominator when using partial fractions?
3. (Tougher) Why are the numerators in Equation 7 (page 499) all constant? (Why does this work?

For Thursday, February 23

1. Give a brief synopsis of the type of integrals encountered thus far.
2. Explain your own personal strategy for attacking an integral. Write as though you were talking to a student studying for a Calc exam.
3. What can we do in class to help you remember this armory of techniques that we have now?

For Friday, February 24

Since we have no new reading for today, pick out three of your favorites from the exercises at the end of Section 7.5, and tell me how you'd approach them.

For Tuesday, February 28

1. How is it possible that the infinite interval on page 530 bounds only a finite area?
2. How can we take one of our bounds of integration to be positive infinity?
3. Explain the Comparison Theorem (page 506) in words.