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Make sure that this examination has 12 pages including this coverThe University of Ontario Institute of TechnologyApril 21, 2006Final Exam:Mathematics 2070U and 2072UNumerical Methods / Computational Science ITime: 3 hoursName :Signature :Student Number :Special Instructions :•Show all your work and calculations.•Use of calculators, course text book, class notes or other hand written notes are permitted.•Use of computer, solutions manual or other text books prohibited.•If you need more space than is provided for a question, use the back of the previous page.•Read each question carefully.Rules governing examinations1. Each candidate should be prepared to produce his or heridentification card upon request.2.Caution :Candidates guilty of any of the following orsimilar practices shall be liable to disciplinary action:(a) Making use of any media that is not specificallyauthorized by the examiners, including cell phonesand pagers.(b) Speaking or communicating with other candidates.(c) Purposely exposing written papers to the view ofother candidates.QGradeMax1102103154105106575810931012Total90
Name:1.(10 marks total)Consider the algebraically equivalent functionsf1andf2given byf1(x) = 1-1 + sin2(x)andf2(x) =-sin2(x)1 +1 + sin2(x)(a)(3 marks)Evaluatef1(x) atx= 0.13 using four-digit rounding decimal arithmetic.(b)(3 marks)Evaluatef2(x) atx= 0.13 using four-digit rounding decimal arithmetic.(c)(2 marks)Assuming that in the absence of round-off error the value (to 6 digits ofaccuracy) of bothf1(0.13) andf2(0.13) is-0.00836750, calculate the relative error forthe values found in parts (a) and (b).(d)(2 marks)