On Monday we completed our introduction to horizontal asymptotes and vertical asymptotes.

On Wednesday we did some examples of curve sketching and applied max/ min problems.

**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*

**Stationary Points are points where the derivative of a differentiable function , .**

**When asked to find the critical points of a function defined on the entire real line (rather than just on a closed interval ), the ‘endpoints’, are not considered critical points.**

**Convex is concave up and concave is concave down.**

Q. 11-17 from http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise4.pdf

*Other Exercise Sheets – ***Questions on Asymptotes**

From section 4 Q. 5 from Problems, find the vertical asymptotes of the the functions 5(b) [(7-10), (13), (15-16), (23)] and Q. 5(c) [except (30-31)]

*Past Exam Papers*

Q. 1 (d) from http://booleweb.ucc.ie/ExamPapers/exams2008/Maths_Stds/MS2001Sum08.pdf

Q. 1(d) from http://booleweb.ucc.ie/ExamPapers/Exams2008/MathsStds/MS2001a08.pdf

Q. 2(a), from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/MS2001Sum06.pdf

Q. 2(a), 6(b) from http://booleweb.ucc.ie/ExamPapers/exams2006/Maths_Stds/Autumn/ms2001Aut.pdf

Q. 2(a) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001.pdf

Q. 2(a), 6(b) from http://booleweb.ucc.ie/ExamPapers/Exams2005/Maths_Stds/MS2001Aut05.pdf

Q. 6(b) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/ms2001s2004.pdf

Q. 6(b) from http://booleweb.ucc.ie/ExamPapers/exams2004/Maths_Stds/MS2001aut.pdf

Q. 6(b) from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/MS2001.pdf

Q. 6(b) from http://booleweb.ucc.ie/ExamPapers/exams2003/Maths_Studies/ms2001aut.pdf

Q. 6(b) from http://booleweb.ucc.ie/ExamPapers/exams2002/Maths_Stds/ms2001.pdf

Q. 6(b) from http://booleweb.ucc.ie/ExamPapers/exams/Mathematical_Studies/MS2001.pdf

*All of this except Q. 1(d) [this is the Autumn 2010 paper which wasn’t on the library website earlier in the year]*

http://booleweb.ucc.ie/ExamPapers/exams2010/MathsStds/Autumn/MS2001Aut2010.pdf

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December 4, 2010 at 10:20 am

RobertHi J.P.

Can you break down for me (if you haven’t done so already) what is and isn’t going to be coming up on the test?

Cheers,

Robert.

December 6, 2010 at 12:23 am

J.P. McCarthyRobert,

Everything we did from Continuity on Intervals up to (but not including) Points of Inflection is examinable.

i.e. p.32 to p.51 of http://irishjip.files.wordpress.com/2010/10/ms2001_notes.pdf.

Note that the both the Closed Interval Method and the First Derivative Test were covered before Points of Inflection [and are hence examinable], in class but are not in these notes.

J.P.