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.
[EDIT] Definition Questions
If you really want to get good at your definition questions check out these (tough) exercises..
Next Week
We will have an additional tutorial instead of a lecture on Monday 24.
This Week
On Monday, we covered from (but not including) Definition 3.1.1 to (and including) Corollary 3.1.6. On Wednesday we went through Questions 1 & 2 from 2010/11’s Test 1 A and we did Q. 3 from the sample test.
Problems
Wills’ Exercise Sheets
Q. 1, 2, 3(i) & (iii), 4, 8(a) & (b) from Exercise Sheet 3.
More Exercise Sheets
Nothing from from Problems.
Past Exam Papers
Nothing from Summer 2010.
Nothing from Autumn 2010.
Nothing from Summer 2009.
Nothing from Autumn 2009.
Q. 4(a) from Summer 2008.
Nothing from Autumn 2008.
Nothing from Summer 2007.
Q. 4(b) from Autumn 2007.
Nothing from Summer 2006.
Nothing from Autumn 2006.
Nothing from Summer 2005.
Nothing from Autumn 2005.
Nothing from Summer 2004.
Nothing from Autumn 2004.
Nothing from Summer 2003.
Nothing from Autumn 2003.
Q. 6(a) from Summer 2002.
Q. 4(b) from Summer 2001.
Q. 4(b) from Summer 2000.
From the Class
- Prove Proposition 3.1.4 (ii).
- Prove Corollary 3.1.6.
Supplementary Notes
We never proved the following in class.
Proposition 3.14
Let be functions that are differentiable at some
. Then
(iii) is differentiable at
with
[Product Rule]
(iv) if , then
is differentiable at
with
[Quotient Rule]
Proof:
(iii)
(iv) Let :
Letting on both sides:
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