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Unformatted text preview: MATH 2070U/2072U Test 5
Instructor: D.A. Aruliah Week 10, 2008
Name (last name, ﬁrst name): Student Number: Teaching Assistant: Instructions
• Before starting, read over the entire test carefully. • Please verify that the test has 5 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 4 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: Mks: 1 6 2 5 3 5 4 4 Total 20 MATH 2070U/2072U Test 5 Page 2 of 5 1. [6 marks] Starting from the interval [a0 , b0 ] = [0, 1], use the bisection method to identify the interval 2 [a2 , b2 ] bracketing a solution of the equation e−x = sin x. That is, carry out two steps of bisection. 1. MATH 2070U/2072U Test 5 Page 3 of 5 2. [5 marks] Starting from the initial iterate x0 = 2, use Newton’s method to ﬁnd the next iterate x1 approximating a solution of the equation x4 = 3x2 + 1. 2. MATH 2070U/2072U Test 5 Page 4 of 5 3. [5 marks] Starting from the initial iterates x0 = 4 and x1 = 6, use the secant method to ﬁnd the iterate x2 approximating a solution of the equation x cos(x) = 2. 3. MATH 2070U/2072U Test 5 Page 5 of 5 4. [4 marks] Supposed you wish to solve the equation ex = x tan x using M ATLAB . Write the relevant commands you would use (using an anonymous function) to ﬁnd a solution assuming you know one exists near x0 = 1.25. 4. ...
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This note was uploaded on 02/23/2010 for the course MATH 2070 taught by Professor Aruliahdhavidhe during the Spring '10 term at UOIT.
 Spring '10
 aruliahdhavidhe
 Math

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