MT1100 Problem Sheet 9 Due: Thursday 3rd December 2020 at 10:00. Please write your name clearly at the top of each page. Scan your work as a single-file PDF. Do not use too high a resolution to ensure the file size remains below 20 MB (the upper limit is 50MB). Then upload your PDF file onto Moodle, as per the instructions available from the General Information box on Moodle. You are encouraged to leave your handwritten comments to the marker on the first or last page of your homework submission. 1. Let g : R -> R be defined by g(x) = (x - 2)2 + 2. (i) Prove, by induction on n, that g(n) (s) = (s - 2)2" + 2. (ii) Find the Julia set Jg of g. Justify your answer. You can use the following fact without proof: For c E R with c ? 0, lim 1700 0 when c < 1, 1 when c = 1, 00 when c > 1. 2. This problem sheet is A4 size. This is one of a sequence of paper sizes (A0, A1, A2, A3, A4, A5 and so on) with the following properties. If you fold a piece of An paper in half, you get the A(n + 1) size. All the sizes are similar rectangles. The area of A0 is one square metre. (i) What is the area (in square metres) of an A4 sheet of paper? (ii) What is the ratio between the lengths of the sides of an A4 sheet of paper? [You need to justify your answers.]