I am emailing a link of this to everyone on the class list every Wednesday morning. If you are not receiving these emails or want to have them sent to another email address feel free to email me at jippo@campus.ie and I will add you to the mailing list.

## Test 2

See here for full details.

## This Week

In lectures, we covered sections 4.3 to Summary 4.5.5 inclusive.

In the tutorial we answered Q. 9 (ii) from Exercise Sheet 1, Q. 10 (iii), 16 from Exercise Sheet 3 and Q.2 from Exercise Sheet 4.

## Problems

You need to do exercises – all of the following you should be able to attempt.

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.

Finding the limit as $x\rightarrow\pm\infty$ means find an asymptotic.

‘Horizontal’ asymptotes are asymptotics.

Convex is concave up and concave is concave down.

Do as many as you can/ want in the following order of most beneficial:

### Wills’ Exercise Sheets

Q. 10 from Exercise Sheet 4.

More Exercise Sheets

Section 4; Q. 3, 4, 5 (a)(i), 5 (b) [NOT (14)-(22) nor (25)], 5(c) [(26)-(29)], 5(d) [(32)-(34)] from Problems.

### Past Exam Papers

Q. 5 from Summer 2010.

Q. 5 from Autumn 2010.

Q. 5 from Summer 2009.

Q. 5 from Autumn 2009.

Q. 5 from Summer 2008.

Q. 5 from Autumn 2008.

Q. 5 from Summer 2007.

Q. 5 from Autumn 2007.

Q 5 (b) from Summer 2006.

Q. 5(b) Autumn 2006.

Q. 5(b), 6(a) from Summer 2005.

Q. 5(b), 6(a) from Autumn 2005.

Q. 5(b) from Summer 2004.

Q. 5(b) from Autumn 2004.

Q. 2(b), 5(b) from Summer 2003.

Q. 3(a), 5(b) from Autumn 2003.

Q. 5(b) from Summer 2002.

Q. 4(a) from Summer 2001.

Q. 4(a)   from Summer 2000.

### From the Class

1. Prove that the derivative of the absolute value function is $-1$ for $x<1$ and $1$ for $x>1$.
2. Prove Proposition 4.5.3
3. Show that
$\lim_{x\rightarrow2}\frac{3x^2-2x+2}{x^2-x-2}=\pm\infty$.

## Supplementary Notes

Some curve sketching.