Sp94ex1 - Problem 3 Consider the function f(x) = x 3 + x -...

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EGN 3420 EXAM I Name________________ Sp 94 SHOW ALL WORK! Problem 1 Consider the function f(x) = x 5 - 1. A) Find an expression for the difference f(x 1 ) - f 2 (x 1 ) where f 2 (x) is the second order truncated Taylor Series expansion of f(x) about some point x 0 . Leave your answer in terms of x 0 and x 1 . B) Evaluate the expression from Part A) when x 0 =1 and x 1 =1.1
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EGN 3420 EXAM I Name________________ Sp 94 SHOW ALL WORK! Problem 2 The function f(x) = x 4 - 10x 2 + 9 has a root located between 2 and 5. Fill in the tables below for the first three iterations of the Bisection Method and the False Position method. Express all answers to four digits after the decimal point. Iteration x l x u x r f(x l ) f(x r ) e A 1 2 5 2 3 Bisection Method Iteration x l x u x r f(x l ) f(x u ) f(x r ) e A 1 2 4 2 3 False Position Method
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EGN 3420 EXAM I Name________________ Sp 94 SHOW ALL WORK!
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Unformatted text preview: Problem 3 Consider the function f(x) = x 3 + x - 1. A) Use the Simple One Point Iteration Method and fill in the table below. Be certain that the g(x) function you choose satisfies the condition g(x) < 0 for all x. i x i x i+1 = g(x i ) 1 2 B) Use the Newton-Raphson Method and fill in the table below. i x i f(x i ) f(x i ) x i+1 1 EGN 3420 EXAM I Name________________ Sp 94 SHOW ALL WORK! Problem 4 Evaluate the following determinant: 1 1 3 2 4 1 7 6 1 2 7 2 1 5--Be sure to show the results of intermediate steps. EGN 3420 EXAM I Name________________ Sp 94 SHOW ALL WORK! Problem 5 Solve the system of equations below by using the inverse matrix. x + z = 1 2y - z = 1 3x + y + 4z = 1...
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Sp94ex1 - Problem 3 Consider the function f(x) = x 3 + x -...

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