# C 1 mark calculate the absolute error of using x 1 to

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(c) [1 mark] Calculate the absolute error of usingX1to approximatex*= 0.3198055582×10-5.(c)(d) [1 mark] Calculate the relative error of usingX1to approximatex*= 0.3198055582×10-5.(d)(e) [1 mark] Calculate the absolute error of usingX2to approximatex*= 0.3198055582×10-5.(e)(f) [1 mark] Calculate the relative error of usingX2to approximatex*= 0.3198055582×10-5.(f)
MATH 2070U/2072UTest 2Instructor: D.A. AruliahWeek 4, 2008Name (last name, first name):Student Number:Teaching Assistant:InstructionsBefore starting,read over the entire test carefully.Please verify that the test has 6 pages.You may use a calculator and a pen or pencil.Test written in pencil are not elegible for regrading.Laptops, cellphones, and pagers are not permitted.Have your student card on your desk.There are 3 questions on this test and a total of 20 marks.There are 45 minutes for the test.Questions do not carry equal weight so use your time wisely.Show as much work as needed to fully answer the questions.Write your answers as neatly as possible in the test itself.You are expected to comply with the UOIT rules for academic conduct.Q:123TotalMks:84820
MATH 2070U/2072UTest 1Page 2 of 61. [8 marks] Convert the following numbers to decimal (i.e., base 10) numbers.Write your answers to at least three digits using the round-to-nearest rule.Use normalised scientific notation with the leading nonzero digit to the right of the decimal point,i.e., in the form(0.d1d2. . . dt)10×10ewhereeis a suitable exponent andd16= 0is the leadingnonzero digit.(a)(110)2(a)(b)(1.11)2×22(b)(c)(22.1)3(c)(d)(1.21)3×3-3(d)
MATH 2070U/2072UTest 1Page 3 of 6(Question 1 continued)(e)(73.4)8(e)(f)(0.175)8×81(f)(g)(C.E)16(g)(h)(0.2A1)16×162(h)
MATH 2070U/2072UTest 1Page 4 of 62. Consider a binary floating-point number system characterised by precisiont= 5and exponents be-tweenemin=-20andemax= 19.(a) [1 mark] What is machine epsilon for this floating-point system?(a)(b) [1 mark] What is the smallest normalised positive machine number (in binary form)?(b)(c) [1 mark] What is the largest normalised positive machine number (in binary form)?(c)(d) [1 mark] What is the (absolute) distance between the machine numbers(1.10010)2×210and(1.10011)2×210?(d)
MATH 2070U/2072UTest 1Page 5 of 63. Consider the quadratic polynomial equationx2+bx+ 1 = 0withb=-0.26753×106. To ten decimal digits, the true value of the smaller of the two positive roots isx*= 0.3737898553×10-5.(a) [2 marks] Use 5 digit rounding arithmetic to calculate the smaller root using the formulaX1:=12-b-pb2-4.(a)(b) [2 marks] Use 5 digit rounding arithmetic to calculate the smaller root using the algebraicallyequivalent formulaX2:=2-b+b2-4.(b)
MATH 2070U/2072UTest 1Page 6 of 6(Question 3 continued)
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