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# MATH 1014 Study Guide - Final Guide: Logistic Function, Conditional ConvergenceExam

Department
Mathematics and Statistics
Course Code
MATH 1014
Professor
All
Study Guide
Final

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Final Examination — April 14, 2012.
MATH1014
Name:
Surname:
Student Number:
Question Mark Obtained
1 (a) (b) (c) (d)
2 (a) (b) (c) (d)
3
4
5
6
7 (a) (b) (c)
8 (a) (b) (c) (d) (e)
9 (a) (b)
Total Mark
Attempt all questions. You are allowed to use non-programmable calculators and refer to notes you
have prepared on a single sheet of 8.5 by 11 inch paper. Use the blank pages provided for rough work,
but show all relevant reasoning in the space provided. The time allowed for completion is 180 minutes.
Total marks: 138

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Final Examination — April 14, 2012.
MATH1014
(1) Determine whether each inﬁnite series is absolutely convergent, conditionally convergent or
divergent. Explain your reasoning in each case by appealing to a relevant fact about inﬁnite
series.
(a)
!
n=1
(1)nn
n+(1)n6 marks
(b)
!
n=210
(1)nn2
2n6 marks

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(c)
!
n=1
n2+2
n
n3+3
n6 marks
(d)
!
n=1
(1)nsin(1/n)6 marks
(2) Let the function F(x)bedenedbyF(x)=
!
n=1
x2n
n2if this series converges.
(a) Ignoring endpoints, what is the interval on which Fis deﬁned? 7 marks