I HAVE TAKEN CARE OF THE DUPLICATE STUDENT NUMBER FOUR DIGIT ENDINGS — ALL OF THESE STUDENTS HAVE RECEIVED AN EMAIL SO YOU DON’T HAVE TO CHECK FOR A DUPLICATE. I HAVE EDITED THE MARK DISPLAY TO TAKE THIS INTO ACCOUNT (the duplicates are last five digits)

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.

## This Week

On Wednesday, we covered from (but not including) Corollary 3.1.6 to Rolle’s Theorem (although we only started the proof).

In the tutorial we answered exercises Q. 1, 3 & 8(a) from Exercise Sheet 3.

## 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. 3, 5, 7, 8 (b), 9 & 10 from Exercise Sheet 3.

More Exercise Sheets

Q. 3 from from Problems.

### Past Exam Papers

Q. 1(c) & 4(b) from Summer 2010.

Q. 1(c) & 4 from Autumn 2010.

Q. 1(c) & 4 from Summer 2009.

Q. 1(c) & 4 from Autumn 2009.

Q. 4(a) from Summer 2008.

Q. 1(c) & 4(a) from Autumn 2008.

Q. 1(c) & 3 from Summer 2007.

Q. 1(c) from Autumn 2007.

Q. 3(b), 4(b) & 5(a) from Summer 2006.

Q. 3(b) & 4(b) Autumn 2006.

Q. 4(a) from Summer 2005.

Q. 4 & 5(a) from Autumn 2005.

Q. 4 from Summer 2004.

Q. 4(b) from Autumn 2004.

Q. 4(b) from Summer 2003.

Q. 4 from Autumn 2003.

Q. 4 & 5(a) from Summer 2002.

Q. 1(b), 5(b) & 6(b) from Summer 2001.

Q. 1(b),  from Summer 2000.

Nothing here.

## Supplementary Notes

The proof of the chain rule and the “chain rule by rule” here.