Problems
You need to do exercises – all of the following you should be able to attempt. Do as many as you can/ want in the following order of most beneficial:
Wills’ Exercise Sheets
Q. 1 (ix), 6, 7, 8 from http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise2.pdf
Past Exam Papers
Q. 3(b) from http://booleweb.ucc.ie/ExamPapers/Exams2008/MathsStds/MS2001a08.pdf
Q. 1(b) from http://booleweb.ucc.ie/ExamPapers/exams2007/Maths_Stds/MS2001Sum2007.pdf
Q. 3(a) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/MS2001Sum06.pdf
Q. 3(a) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/Autumn/ms2001Aut.pdf
Q. 2(b), 3(a) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001.pdf
Q. 3(b) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001Aut05.pdf
Q. 1(b), 3(b) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/ms2001s2004.pdf
Q. 2(b) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/MS2001aut.pdf
Q. 2(b) from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/MS2001.pdf
Q. 2(b) from http://booleweb.ucc.ie/ExamPapers/exams2001/Maths_studies/MS2001Summer01.pdf
Q. 2(c) from http://booleweb.ucc.ie/ExamPapers/exams/Mathematical_Studies/MS2001.pdf
From the Class
1. Recast the definition of a continuous function (at a point) in terms of –
.
2. Prove Proposition 3.3.2 using the Calculus of Limits
2 comments
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October 21, 2010 at 10:57 am
Aileen O Mahony
J P,
For exercise sheet 1, Q7 part (iv) do you bring over the underneath inequality and square both side inc the 5?????
Regards
Aileen
October 21, 2010 at 11:08 am
J.P. McCarthy
Aileen,
That’s exactly what you do.
What makes it possible are the facts that
1.
for all
,
(so you can split the left)
2.
(so you can “bring over the underneath” i.e. multiply across by
as it is positive)
3.
and
then
. Apply this with
and
to get
(i.e. you can square both sides if both sides are positive)
4. Finally
and
(you must square the 5 also).
J.P.