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

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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 .
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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.
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Su 97 EGN 3420 Exam 1 Name ____________________
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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....
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Su97ex1 - SHOW ALL WORK Problem 3(25 pts Display all...

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