ASSIGNMENT 8 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 19. 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 A8, 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 Calculus: Early Transcendentals text, complete question 72 from section 3.3 and question 72 from section 3.6. 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. Let f1 , f2 , . . . , fn be n differentiable functions. Prove that 0 (f1 f2 · · · fn ) = f10 f2 f3 · · · fn + f1 f20 f3 · · · fn + · · · + f1 f2 · · · fn0 . 2. Find the derivative of f (x) = esin(cos x) + 2x x−1 1000 . 3. A nuclear detonation at ground level emits a blast wave that expands radially, like a circular ripple, at a speed of 30 km/second. Find the rate of expansion of the area contained within the blast wave 0.1 seconds after detonation.