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TEST-1-Answers - TEST WEEK 1 ENGR 3723 PROBLEM 1(10 points...

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TEST WEEK 1 ENGR 3723 PROBLEM 1 (10 points) State the difference between chopping, rounding and truncation error ANSWER: -“One method of approximation [of a number] would be to merely omit, or “chop-off”, … higher terms” - Chapra and Canale- 5 th Ed., Page 73. -Rounding is when the last digit of the approximation of a number is chosen to be the lowest or the highest approximation of the remainder, depending on whether this remainder is lower or higher than 0.5 10 -(n+1) , where n is the last significant digit used. -“Truncation errors are those that result from using an approximation in place of an exact mathematical procedure” - Chapra and Canale- 5 th Ed., Page 73 PROBLEM 2 (15 points) a) Determine the number of terms needed to approximate e -x to 5 significant figures. For x=1.3. Use .... ! 4 ! 3 ! 2 1 4 3 2 + + = x x x x e x ANSWER: Term Value of Term Series Significant figures x 1 -0.3 -0.3 0 ! 2 / 2 x 0.845 0.545 0 ! 3 / 3 x -0.36616666666 0.17883333333 0 ! 4 / 4 x 0.11904167 0.2978375 1 ! 5 / 5 x -0.030941083 0.266896417 1 ! 6 / 6 x 0.006703901 0.273600318 2 ! 7 / 7 x -0.00124501 0.272355308 3 ! 8 / 8 x 0.000202314 0.272557622 4 ! 9 / 9 x -0.0000292232 0.272528399 4 ! 10 / 10 x 0.00000379901 0.272532198 5 ! 11
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