Mws you may be asked to submit both these lab 7

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Unformatted text preview: timate that is accurate up to 10 decimal places! You can now appreciate that Newton’s Method is much more efficient (when it works!) at finding roots than the Bisection Method. CAUTION: Newton’s Method can FAIL under certain circumstances (see the assignment in this lab). The Bisection Method, though inefficient, always works. x Copyrighted by B.A. Forrest ([email protected]) 6 Newton’s Method in Maple Lab 7 Exercises Complete the following exercises in a Maple worksheet and write your answers where indicated below (if applicable). Save the worksheet as lab7.mws. You may be asked to submit both these Lab 7 Exercise pages and the printout of lab7.mws during the course. 1. Create the following text input. At the top of a new Maple worksheet, type the following lines in a text region. Maple Lab 7: Bisection Method and Newton’s Method Name: ID: Type your name here. Type your ID here. Date: Type today’s date here. You can enhance the fonts in any way you wish (e.g., change the font, fontsize, bold, etc.) Insert an execution group after the last line of the text region. Enter Maple’s restart: command. 2. Complete the following steps to use the Bisection Method and Newton’s Method to approximate the solution of f (x) = ex + 3x. You will then compare the efficiency of these two methods. a) In Maple, create a text region and enter the following sentence: Bisection Versus Newton’s Method. Insert an execution group (command prompt) after the text region. b) In Maple, create the function f (x) = ex + 3x. HINT: remember that ex is exp(x) in Maple. c) Plot the graph of f (x) using the ranges x = −10..10 and y = −10..10. d) Study the plot you created. How many solutions (roots) does f (x) have? ANSWER: e) Using the Intermediate Value Theorem, explain why there is a root c in the interval [−1.0, 0]. ANSWER: f ) Edit the loop that was presented in this lab on page (vi) for the Bisection Method and enter it in Maple to find an estimate for c with an error of at most 10−6 . (Hint: You will have to edit the lines in the loop so that a := -1.0, b := 0 and e := 10∧(-6). To have an error of at most 10−6 means to be accurate to 5 decimal places. ) ANSWER: ESTIMATE FOR C: g) How many iterates of the Bisection Method did i...
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