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

This preview shows pages 1–5. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 )....
View Full Document

## 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.

### Page1 / 5

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online