• There will be a problem where you are given the graph of a function f, and you will be required to draw the graph of an antiderivative F of  f.
• There will be several problems where you will need to compute indefinite and definite integrals.
• You will have a word problem involving motion under uniform acceleration.  You may need to be careful about converting units (seconds, hours, miles, feet, etc.) to make them consistent.
• You will have a problem where you will need to use the second fundamental theorem of calculus.

The second exam
The exam will be closed book, closed notes, although you will be able to use your calculator and your computer to check answers.  There will not be a problem involving tables of integrals, although I suggest you memorize formulas 1, 2, 3, 5, 6, and 24 on the back jacket of the book, and know how to derive formulas 4, 8, and 14.

• There will be a problem that has several indefinite and definite integrals that you will need to evaluate, using integration by parts, substitution, a partial fraction decomposition, or a combination of these techniques.  You will need to carefully write down each step in the solution process.
• There will be a problem with a couple of improper integrals.  You will need to show whether or not these converge, and you will need to find the limit of those integrals that do converge.
• There will be a problem with a couple of improper integrals whose integrands do not have closed form antiderivatives.  You will need to use comparison tests to show whether or not these converge.

PDF copy of the second exam
Answers, page 1
Answers, page 2
 
 

The third exam
This exam will be open book, open notes.  It will consist of three word problems.  It will be advantageous to know how to compute integrals, approximately and exactly, with your calculator or with Mathematica.  The problems will be from the following five types.

• There may be a problem dealing with arc length.
• There may be a problem dealing with pressure and force.
• There may be a problem dealing with the total weight of an object.
• There may be a problem dealing with center of gravity.
• There may be a problem dealing with work.

PDF copy of the third exam
Answers, page 1
Answers, page 2
Answers, page 3

PDF copy of the third exam, second try
Second try answers, page 1
Second try answers, page 2
Second try answers, page 3

The fourth exam
The exam will be closed-book, but you may use your calculators and the computers.  There will be five problems, of the following types.

1. You will need to write down the first few terms of a Taylor series, from the definition.  The series possibly may not be centered at 0.
2. You will need to compute the radius of convergence of a power series.
3. You will need to write down the first few terms of a Taylor series by using substitution, term-by-term multiplication or division, etc.
4. There will be a word problem involving a geometric series.
5. You will need to compute a bound on the error in a particular Taylor polynomial approximation over a particular interval (using the formula presented in class).

The final exam
The exam will be closed-book, but you may use your calculators and the computers.  There will be nine problems.  To study, you should look over your homeworks and previous exams.  Pay careful attention to the following items.

1. Understand the graphical interpretation of derivatives and antiderivatives, as you saw on the first exam.
2. You will need to compute definite and indefinite integrals, as well as some improper integrals.
3. You will need to carefully use comparison tests to determine whether certain improper integrals converge.
4. You will need to compute the volume of a solid of revolution.
5. You will need to use Taylor series approximations in a practical problem, such as you see in Example 6 and in problems 25 through 27 of section 9.3 of the book.
6. You will need to compute a bound on the error in a Taylor polynomial approximation, based on the error formula I introduced in class.
7. You will need to find the solution to a simple initial value problem.  (See section 10.4 of the book.)
8. You will need to solve a practical problem such as those in section 10.5 of the book.