Section B.9 Problem Sheet 9
Due 24 April at 4pm, either in class or in the pigeon hole in 4W.
Exercise 5.2.1 is a straightforward calculation which should give you a bit of practice thinking about these reflections, which we will be using constantly in Section 5.4.
Exercise 5.3.1 is a reminder of an important difference between Lemma 5.4 and, e.g., Proposition 3.4.
This year I’ve decided not to assign Exercise 5.4.1, which is needed to complete the proof of Lemma 5.6 in the more difficult case where \(f(0) \lt 0\text{.}\) It’s a good exercise to attempt, though, if you’re feeling rusty with multivariable calculus and want some practice.
Exercise 5.4.2 and Exercise 5.4.3 are classic exercises to get you thinking about how the steps in the proof of Theorem 5.1 fit together. Do not worry too much about writing these up in complete detail.
We will have one more sheet after this one, as outlined in the Weekly schedule.
Please feel free to email me, or drop by office hours (Wednesdays 1:15–2:05 in 4W 1.12). I am also more than happy to meet one-on-one or in a small group.
