Sp99ex1 - 0.7500 2 3 4 5 6 7 8 False Position Method Sp 99 EGN 3420 EXAM I Name SHOW ALL WORK Problem 3(25 pts Solve the system of equations Ax b =

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Sp 99 EGN 3420 EXAM I Name________________________ SHOW ALL WORK! Problem 1 (25 pts) Given the function f x e x x ( ) sin = - , a) Find f 2 ( x ), the second order truncated Taylor Series Expansion of the function about the point x 0 . Leave your answer in terms of x and x 0 . Note: Your final answer should not be f x f x f x x x f x x x 2 0 0 0 0 2 2 ( ) ( ) ( )( ) ( ) ( ) = + - + ′′ - b) If x 0 = π /2, then the quadratic function f 2 ( x ) can be expressed as f x a a x a x 2 0 1 2 2 ( ) = + + where a a a 0 1 2 , , and are constants. Find a a a 0 1 2 , , and and leave your answers in terms of π .
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Sp 99 EGN 3420 EXAM I Name________________________ SHOW ALL WORK! Problem 2 (25 pts) Consider the function f(x ) = ( x - 0.4)e x – 2.5 x + 1. Fill in the tables below using the Bisection Method and the False Position method. Stop when the |e A | falls below 5%. Express all answers to four digits after the decimal point. i x l x u x r f ( x l ) f ( x r ) | e A |, % 1 0.0000 1.5000 2 3 4 5 6 7 8 Bisection Method i x l x u x r f ( x l ) f ( x u ) f ( x r ) | e A |, % 1 0.0000
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Unformatted text preview: 0.7500 2 3 4 5 6 7 8 False Position Method Sp 99 EGN 3420 EXAM I Name________________________ SHOW ALL WORK! Problem 3 (25 pts) Solve the system of equations Ax b = by finding A-1 and then using x A b =-1 . Leave all answers in terms of fractions. Use the method of cofactors to find A-1 . x-2z = 2x + 3y + 4z = 3 36x-60y + 12z = 1 Sp 99 EGN 3420 EXAM I Name________________________ SHOW ALL WORK! Problem 4 (25 pts) a) Apply the Newton-Raphson method to find the root of the function f x x x ( ) =-16 3 starting with an initial guess of x =1. Compute the approximate and true relative errors, expressed as a percent, at the completion of the 3 rd iteration. Express all answers to 4 places after the decimal point....
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This note was uploaded on 06/09/2011 for the course EGM 4320 taught by Professor Klee during the Spring '11 term at University of Central Florida.

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Sp99ex1 - 0.7500 2 3 4 5 6 7 8 False Position Method Sp 99 EGN 3420 EXAM I Name SHOW ALL WORK Problem 3(25 pts Solve the system of equations Ax b =

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