Math 1297 Calculus II
Test 3 info
Spring 2007
Prof. Peckham
 Location: Montague 80. Sit in alternate seats starting from the outside.
 Time: 12:551:50 Friday April 27.
 Sections covered: 12.112.10, 12.12, 15.1.
 General Info: The test will have between 15 and 20 problems.
Most,
but not necessarily all,
will be similar to Homework or Quiz problems.
 Students will be allowed to use calculators which do not have the
capability of symbolic manipulation. For example, the TI 89 is not allowed
for the test. Students should indicate on their solutions any place a calculator
has been used. The test will be written so that a calculator is not necessary.
Certain questions will require "exact answers" (as opposed to decimal
approximations obtained by calculator) for full credit.
Formulas. You should know the Taylor series for 1/(1x) since it is the geometric series.
Any other series you need I will provide the formula.
(You will, of course, be asked in at least one problem to compute the first several terms in a Taylor series formula for some function.
You are not expected to know the coefficients in advance.
In fact, you will not receive full credit unless you show how you obtain the coefficients from the Taylor series formula.)
You should also know the formula for the upper bound on the remainder (formula 9, p. 799).
 Study suggestions
 Review HW's, Quizzes, practice test.
For a PDF version of the practice
problems select here.
 End of chapter review material:
 Ch. 12: Concept Check problems 111; TrueFalse Quiz problems 118.
 Ch. 15: Concept Check problems 1.
 Definitions required to know:
 The "epsilonN" definition of what it means for a sequence {a_{n}} to converge to L. (Definition 1 on page 739)
 The definition of what it means for the series
a_{1}+a_{2}+a_{3}+... to converge to S. (You will need to first define the nth partial sum s_{n}.) (Definition 2, page 750)
 Absolute convergence of a series; conditional convergence of a series.
 Proofs required to know:

Prove that a specific geometric series converges to a specific limit
directly from the definition. That is, compute a formula for the nth
partial sum s_{n} and take its limit as n goes to infinity. See
practice test problem #20 for example.
 Prove that if a series converges, the individual terms must converge to zero. (Theorem 6, p 754)
 Prove the basic comparison test for nonnegative convergent series (p. 767, part i)
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