MATH 152 Practice Final Exam Winter 2017 Final Exam: Tuesday, March 21st 10:30am-12:30pm, SAM 102 Notes: Graphing calculators will be allowed. Please bring pencils and erasers. Make sure you show all work! You may use a calculator to evaluate a definite integral only if the question states you are allowed to do so. You will also be permitted to bring a two-sided sheet of paper with any formulas, theorems, etc. Only a standard size piece of paper will be allowed (8.5 x 11 inches). Anyone who violates these requirements will not be allowed to use their formula sheet during the final exam! Exam Format: The exam will be two parts. Part I. Recent Material: Ch. 6.1 - 6.4 and work Ch. 6.6, Ch. 7.1 - 7.3 (omit 6.3): 5 questions Part II. Review Material: Ch. 5 material (main ideas/ applications): Choose 1 question (out of 2). Practice Part I. 1.) (Ch. 6.1) Let be the region bounded by the graphs of = sin() and = 3 4 shown below. Find the area of the region . 2.) (Chapter 6.4) Find the exact length of the curve: = cos(3) , = sin(3), 0 /2. 3.) (Chapter 6.2 and 6.3) Consider the region bounded by the curves = 3 , = 5, and = 0. 3A.) Find the volume of the solid obtained by rotating the region about the line = 6. 3B.) Find the volume of the solid obtained by rotating the region about the -axis. 4.) (Chapter 6.3) Consider the region bounded by the curves = 2 and = 3 . Find the volume of the solid created by rotating this region about the -axis. 5.) (Chapter 7) 5A.) Solve the separable differential equation: = 5B.) Find a solution of the differential equation above that satisfies the initial condition, (0) = 1. 5C.) Choose the correct direction field for the differential equation. On the correct direction field, sketch the graph of the solution that satisfies the initial condition (0) = 2. y 4 y 4 4 2 2 2 2 4 x 4 2 2 2 2 4 4 4 6.) (Ch. 6.6) A 300 lb. cable is 150 feet long and hangs vertically from the top of a tall building. How much work is required to lift the cable to the top of the building? x 7.) (Ch. 7.3) A tank contains 1000 L of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after 20 minutes? Practice Part II. 1.) A honeybee population starts with 100 bees and increases at a rate of () = 2 + 16 bees per week. A.) What does 100 + 0 () with a constant, represent? B.) Find the total bee population after 10 weeks. Show all work done to evaluate the definite integral. Do not use a calculator to evaluate the integral! 2.) A particle is traveling with velocity function () = sin5 cos 3 (m/ 2 ). 2A.) Find the particle's displacement during the first /2 seconds. 2B.) If the particle started at the origin, find the particle's position function ()