MT1100 Problem Sheet 7 Due: Thursday 19th November 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. For what values of k is the conic 3x2 + 5y2 - 18x + 4y = k (a) an ellipse, (b) a single point, (c) a curve with no points? [Hint: Think of k as a constant, and try bringing the equation into standard form.] 2. Let a and b be constants, with a # 1. Let f : R -> R be defined by f(x) = ax +b. Prove by induction that for any positive integer n, f(n)(x) = a"x + - " +" = 1, a- 1 a" - 1,