MCS-122 - Calculus II
Fall 2006:
Exam 3 Review
Exam location & times: Olin Hall 103,
either 5:30-7:25 or 7:30-9:25,
on Tuesday evening, November 14, 2006.
General Rules
-
You are allowed one new 3"-by-5" note card with anything
you wish written on both sides for use during the exam.
You may also use your 3"-by-5" note cards from Exams 1 and 2.
-
No other notes or books are allowed at the exam.
-
You must have your graphing calculator with you, with angular measure set
to radian mode.
Suggested Exam Study Tactics
-
Look over your old homework assignments and in-class exercises.
-
Do a few the review problems in the links below and do the
"Check Your Understanding" true/false problems.
Answers are posted
outside my office.
Also look at odd-numbered problems in the Review Exercises and Problems
at the end of each chapter.
-
Master the ideas given in the document
"Testing Series
for Convergence";
summarize the information on your note card.
-
Think carefully about what else you want to write on your one note card.
What the exam will cover
Chapter 9: Sequences and Series
- Sequences
- Geometric series
- Convergence of sequences and series
- Tests for convergence
See list given in class.
- Power series
Chapter 10: Approximating Functions Using Series
(excluding Sect. 10.5: Fourier series)
- Taylor polynomials
- Taylor series
- Finding and using Taylor series
- The error in Taylor polynomial approximations
Standard problems
(Be prepared also to think about nonstandard problems.)
- Does a given series converge, i.e., have a "sum"?
- What is the sum--exactly or approximately?
- How many terms of a series must be added to approximate the sum
within a given accuracy?
- For which values of x does a given power series converge?
- What is the Taylor polynomial approximation Pn(x) of
a given function?
- What is the Taylor series of a given function?
- What is a bound on the error made in using a Taylor polynomial to
approximate a given function at a given point or over a given interval?
- What order (degree) of Taylor polynomial approximation should you
use to approximate a given function to within a given accuracy?
- Prove that a given function equals its Taylor series (if true).
- Explain what is meant by: infinite series, power series,
partial sums, sum of a series, convergence, divergence,
Taylor polynomial, Taylor series.
- True/false problems of the "Check Your Understanding" type
-
Outline of convergence testing
Suggested Review Problems
-
Problems on convergence of series
(ps)
(pdf)
-
Solutions of problems on convergence of series
(ps)
(pdf)
- Power series problems
(ps)
(pdf)
- Power series solutions
(ps)
(pdf)
- Taylor polynomials and series:
10.1: #7, 13, 35; 10.2: #7, 21; 10.3: #5, 15;
10.4: #5, 11; Ch. 10 review: #19, 21
- Answers are in the back of our text.
Last modified: 11/13/06