ASSIGNMENT 9 for SECTION 001 There are three parts to this assignment. Part A is to be completed online before 7:00 a.m. on Friday, November 26. Part B and Part C, which require full solutions, are to be handed in at the beginning of class on the same date. Part A [10 marks] This part of the assignment can be found online, labelled A9, at webwork.elearning.ubc.ca — sign in using the MATH110 001 2010W button. Part B [5 marks] This part of the assignment is drawn directly from the course texts. It focuses on mathematical exposition; you will be graded primarily on the clarity and elegance of your solutions. From the Just-In-Time text, complete question 10 from section 7.4. From the Calculus: Early Transcendentals text, complete question 54 from section 3.4. Part C [15 marks] This part of the assignment consists of more challenging questions. You are expected to provide full solutions with complete arguments and justifications. 1. Prove that there are an infinite number of lines through the origin tangent to y = cos x. 2. Describe all the points where the curve y = cos 3. Let 1 x has horizontal tangent lines. 1 for x < 1 (x − 1) sin x − 1 f (x) = g(x) for 1 ≤ x ≤ 2 . x e for x > 2 Find a function g(x) such that f (x) is continuous everywhere. You must justify your answer.