Su97ex1 - SHOW ALL WORK! Problem 3 (25 pts) Display all...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Su 97 EGN 3420 Exam 1 Name ____________________ SHOW ALL WORK! Problem 1 (25 pts) Consider the function f(x) = xe x . At x=1, the difference between the 2 nd order Taylor Series expansion of f(x) about some pt x 0 and the 1 st order Taylor Series expansion of f(x) about the same pt x 0 is equal to ¼. 1. Find an equation that can be used to solve for x 0 . 2. Perform 2 iterations of the simple one point iteration method to determine x 0 .
Background image of page 1

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

View Full DocumentRight Arrow Icon
Su 97 EGN 3420 Exam 1 Name ____________________ SHOW ALL WORK! Problem 2 (25 pts) Display all answers to 3 places after the decimal point! a) Apply the Bisection method to find the root of the function f x x x ( ) = - 16 3 located between x l =1 and x u =4. Compute the approximate and true relative errors expressed as a percent at the completion of the 3 rd iteration. b) Repeat Part a) using the Newton-Raphson method starting with an initial guess of x 0 =1.
Background image of page 2
Su 97 EGN 3420 Exam 1 Name ____________________
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: SHOW ALL WORK! Problem 3 (25 pts) Display all answers to 3 places after the decimal point! a. Find the equation of the Lagrange polynomial that passes thru the data points (0,-2), (1,0), (2,2) and (4,6) taken from an unknown function f(x). b. Use the polynomial for interpolation at x=3. c. Compute the true error under the assumption that the true function f(x) is linear. Su 97 EGN 3420 Exam 1 Name ____________________ SHOW ALL WORK! Problem 4 (25 pts) Display all answers to 3 places after the decimal point! 1. Fit a second order Newton’s interpolating polynomial f 2 (x) thru the data points (-1, e-1 ), (0,1) and (1,e) from an unknown function f(x). 2. Evaluate the resulting polynomial at x=0.5 3. Estimate the error in f 2 (0.5) by using an additional point at (2,e 2 ). 4. Can we determine the true error at x=0.5? Explain....
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 / 4

Su97ex1 - SHOW ALL WORK! Problem 3 (25 pts) Display all...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online