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Last name (Print):First name (Print):UW Student ID Number:University of WaterlooFinal ExaminationMath 118(Calculus 2 for Engineering )Instructor:See table belowSection:See table belowDate:Wednesday, August 10, 2011Time:9:00 to 11:30 a.m.Term:1115Duration of exam:2.5 hoursNumber of exam pages:13Exam type:Closed Book(including cover page)Additional material allowed:NoneCircle your instructor’s name and section numberInstructorSectionC. D. Roberts001CHE studentsR. Andr´e002Geo-Env. studentsR. Andr´e003Mechanical studentsN. K. Soontiens004Mechatronics studentsInstructions1. Please be sure your name and ID numberappear correctly at the top of this page.2. Answer the questions in the spaces provided,using the backs of pages for overflow orrough work.3. To obtain maximum marks show all yourwork, carefully justifying your answers.4. The use of calculators or any other aids willnot be allowed for the test.FOR EXAMINERS’ USE ONLYQuestionMark1/42/73/44/95/46/47/38/59/510/811/612/413/314/9Total/75Formulas:•sin 2α= 2 sinαcosα•sin2α= (1-cos 2α)/2•cos2α= (1 + cos 2α)/2