Sp01ex1 - Stop when the approximate relative error is less...

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Sp 01 EGN 3420 EXAM 1 Name________________ Show all Work! Problem 1 25 (pts) Consider the function ( ) cos f x x x = . A) The first order truncated series of f ( x ) about a point x 0 can be written as 1 0 ( ) ( ) f x a b x x = + - Find expressions for a and b in terms of x 0 . B) Find the truncation error ) ( ) ( 1 x f x f E T - = at x = 12 π if x 0 = 0.
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EGN 3420 EXAM 1 Sp 01 Problem 2 (20 pts) The function ( ) cos f x x x = has a root located in the interval 1 2 x . Fill in the table 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 1.0000 2.0000 2 3 The function ( ) cos f x x x = has a root located in the interval 4 5 x . Fill in the table below for the first three iterations of 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 (%) e T (%) 1 4.0000 5.0000 2 3
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EGN 3420 EXAM 1 Sp 01 Problem 3 (15 pts) Use the Simple One Point Iteration Method to find the root of 1 2 ( ) 2 1 0 f x x x = + - = . Fill in the table below. Round all numerical answers to 4 places after the decimal point.
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Unformatted text preview: Stop when the approximate relative error is less than 20 % or the table is full, whichever occurs first. Be certain to show what g ( x ) is. i x i e A (%) 0.0000 1 2 3 4 5 EGN 3420 EXAM 1 Sp 01 Problem 4 (20 pts) For the following system of equations Ax b = 1 2 3 4 1 3 4 1 2 3 4 2 3 4 3 2 3 8 25 2 5 x x x x x x x x x x x x x x + + + =-+-=-+-= +-= A) Show that the determinant of the matrix A is not zero. Do not use a calculator. B) Use the Gauss Jordan Method to find the solution. EGN 3420 EXAM 1 Sp 01 Problem 5 (20 pts) In the system of equations below 1 2 3 4 1 2 3 4 1 2 3 4 2 3 4 3 1 2 2 2 3 8 12 10 x x x x x x x x x x x x x x x K + + + =-+ +-=-+-= + + = Find the value of K which produces an infinite number of solutions. Hint: Look at the Echelon Form of the augmented matrix (A|b )....
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Sp01ex1 - Stop when the approximate relative error is less...

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