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# Fa98ex1 - Fa 98 Problem 3(25 pts Consider the equation f x...

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Fa 98 EGN 3420 EXAM I Name________________ Show all Work! Problem 1 25 (pts) Consider the function f x e x ( ) . = A) Find an expression for f 2 ( x ), the 2 nd order truncated Taylor Series expansion of f( x ) about a point x 0 . Leave your answer in terms of x 0 . B) Find the truncation error E f x f x T = - ( ) ( ) 2 at x = 1.1 x 0 . Leave your answer in terms of x 0 . C) Find the truncation error when x 0 = 1 and x =1.1

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EGN 3420 EXAM I Fa 98 Problem 2 (25 pts) The function f x e x x x ( ) ( ) ( ) = - - - 1 1 has a root located between 0.5 and 2. Fill in the tables below for the first three iterations of the Bisection 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 (%) e T (%) 1 0.5000 2.0000 2 3
EGN 3420 EXAM I

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Unformatted text preview: Fa 98 Problem 3 (25 pts) Consider the equation f x xe x ( ) . =-= 2 0 Use the Simple One Point Iteration Method to find the root of f x ( ) . = Let g x e x ( ) =-2 and fill in the table below. Round all numerical answers to 4 places after the decimal point. i x i 0.0000 1 2 3 4 5 EGN 3420 EXAM I Fa 98 Problem 4 (25 pts) Consider the function f x e x ( ) . =-2 The Newton-Raphson Method is used to find the root of f x ( ) . = a) The initial guess is x . Express x 1 in terms of x . Do not leave your answer in terms of f x f x ( ) ( ). and ′ b) Find x , if x 1 = x + 1....
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Fa98ex1 - Fa 98 Problem 3(25 pts Consider the equation f x...

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