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EGN3420F97Test1

# EGN3420F97Test1 - f x x 2 11 does not converge when g x x f...

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EGN 3420 Test #1 Fall 1997 4:30 - 5:45 PM Open notes, open book and can use calculator. Write on test sheets. Use the back of the sheet if necessary. Show all work for partial credit and explain how you are going to solve the problem. NAME__________________________________ SS#_______________________________________ #1 (20%) Find the positive root of the function f( ) x x 3 . 3.5 x 2 . 21.0 x 67.5 . Use a bracket method first to find an initial approximation then use a faster converging method to further improve your estimate to 2 digits of accuracy. 1000 0 1000 10 0 10 0 f( ) x x

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#2 (20%) Use Newton’s method to find the higher root of f( ) x x 2 . 7 x 12 . Find to 2 digits of accuracy. 10 0 10 20 5 0 5 10 0 f( ) x 0 x
#3 (15%) Find 11 to 4 digits of accuracy (i.e. 3.317). Unlike the home work, this time use a method that works and converges. Recall from the home work that

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Unformatted text preview: f( ) x x 2 11 does not converge when g( ) x x f( ) x . Perhaps f(x) will converge with a different g(x). #4 (15%) Let x = 45.9688 and y = 45.9445. If our computer can only store 4 digits, what is the relative error for x and y when we represent the numbers using our computer. Compute z = (x - y) + 0.01946. What is the relative error of z. How many digits of significance does z have. #5 (15%) What is the rate of convergence for f(n). f(n) converges to 0 but at what rate O(?). Recall α n converges to α with rate β n if α n α . β n k for some constant k f( ) n . ( ) n 2 ( ) n 4 n 3 #6 (15%) What is the error of f(x,y) if x = 5 and y = 2 where x has an error of 10% and y 50%. f( ) , x y x 2 x 6 . 1 10 y...
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EGN3420F97Test1 - f x x 2 11 does not converge when g x x f...

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