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Sp95ex2B - 6 2 1 a I dx x = Using Trapezoidal...

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Sp 95 EGN 3420 Exam 2B Name___________________ SHOW ALL WORK! Problem 1 (25 pts) Solve the following system of equations using the Gauss Jordan Elimination Method. a + b + c + d = 5 2a - b - c + d = 25 a + 3b + 2c - 4d = 0 2b - 2c + d = 10 (A|b ) = 1 1 1 1 2 1 1 1 1 3 2 4 0 2 2 1 5 25 0 10 - - - -
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Sp 95 EGN 3420 Exam 2B Name___________________ SHOW ALL WORK! Problem 2 (25 pts) Find the equation of the Least Squares line which best fits the hyperbola y = 1/x over the interval (1,5). Do this by generating 5 equally spaced points over the interval (1,5) from the hyperbola. Find the sum of the squares of the residuals SSE. Round all calculations to 4 places after the decimal point. i x i y i = 1/x i 1 1 1.0000 2 2 3 3 4 4 5 5
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Sp 95 EGN 3420 Exam 2B Name___________________ SHOW ALL WORK! Problem 3 (25pts) Consider the definite integral
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Unformatted text preview: 6 2 1 a I dx x = ∫ . Using Trapezoidal integration with a step size ∆ x =1 results in an approximate value I T = 2.44375. A) Find the value of “a”. B) Using the correct value of “a”, apply Simpson’s 1/3 Formula with ∆ x =5/6 and find I S , the approximation to the definite integral. C) Find the true relative error in Parts A) and B). i x i 2 i i a f x = 1 2 3 4 5 Sp 95 EGN 3420 Exam 2B Name___________________ SHOW ALL WORK! Problem 4 (25pts) Using Trapezoidal integration to approximate the definite integral 4 sin I xdx = ∫ it is necessary to keep the truncation error below 2.854785 x 10-8 . Find the number of required sub-intervals from 0 to π /4....
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