Page 458 - Excel for Scientists and Engineers: Numerical Methods

APPENDIX 8 ANSWERS AND COMMENTS FOR PROBLEMS 43 5

9. After evaluating the areas using a trial value of c, Goal Seek.. . was used to
set the relationship area bounded by y=4 - 2* area bounded by y = c to
zero. The changing cell and the target cell are shown on the spreadsheet. c =
2.528.

10. The same procedure was followed as in the preceding problem. c = 8.68

11. Answer = 6.51413 (approx.), n4/15 = 6.493939 (exact).
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12. (a) Answer: 1 (b) 1 (c) !h (d)

Chapter 8 Roots of Equations

1. To find the first time after t = 0 when the current reaches zero, you must
begin with a value oft 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.

2. Use Goal Seek.. . D = 0.756.

3. The spreadsheet shows a manual method, similar to the interval-halving
method, and also uses Goal Seek. [Ba2'] = 1.28 x 1 0-5 M.

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

5. Use Goal Seek with Yl-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: x = -5.857 and x = 12.494.

6. Follow same procedure as in the preceding problem. For h = 0.5, x = -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..

8. x = 0.288, [A] = 0.4858 mol L-I.
9. x = 0.8598, [A] = 0.1402 atm