## Chapter Roots of Equations

1. To find the first time after t = 0 when the current reaches zero, you must begin with a value of t that will force Goal Seek to converge to the first i = 0 after t = 0. Using t = 1 is a good choice, t = 1.576 seconds.

3. The spreadsheet shows a manual method, similar to the interval-halving method, and also uses Goal Seek. [Ba2+] = 1.28 x 10"5 M.

4. The spreadsheet shows the graphical method and also uses Goal Seek. S = 0.13 mol/L.

5. Use Goal Seek with Y1-Y2 as target cell formula Use two different initial values of x to get the two different x-values. Formulas are under the chart. Answer: jc = -5.857 and x = 12.494.

6. Follow same procedure as in the preceding problem. For h = 0.5, jc = -0.87 and x = 0.87. If you use the Goal Seek custom function, you can change the value of h and observe the intersections change.

7. This problem requires two successive uses of Goal Seek. The procedure is described on the spreadsheet..

11. I used Goal Seek... with the cell containing the formula MDETERM as the target cell and the cell containing the (1,1) element of the matrix as the changing cell. The cell value 0.25 gives a determinant value of zero. Two elements of the matrix cannot be varied so as to give a zero value: the (1,3) element and the (3,1) element.

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