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.


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 a\in\mathbb{R} where the derivative of a differentiable function f:\mathbb{R}\rightarrow\mathbb{R}, f'(a)=0.

When asked to find the critical points of a function defined on the entire real line (rather than just on a closed interval [a,b]), the ‘endpoints’, \pm\infty 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]