Page 457 - Excel for Scientists and Engineers: Numerical Methods

434 EXCEL: NUMERICAL METHODS

6. (a) F'(x) = 0.1 1072 at x = -4, 0 at x = 0.
(b) F'(x) = 9.0028E-07 at x = -4.
(c) F'(x) = 0 at x = 0, -0.5 at x = 1.
(d) F'(x) = 0 at x = 1, -0.01 176 at x = 10
(e) F'(x) = 0.00242 at x = 90, -2E-10 at x = 100.

7. I used the custom function to calculate the first derivative. For a = 1, the
mid-point slope was 0.25.

8. I used the custom functions dydx and d2ydx2 to calculate the first and second
derivatives. Errors were all in the range lo-' to lo-'.

Chapter 7 Integration

1. Area = 2.4 105 (approx.).
1
2. (a) Answer: - (b) 0.746824133375978 (c) 2
l+n

(g) 0.287682

3. Answer given in a table: 1.3506.

4. Answer: 5.864 (approx.), 5.877 (exact).

5. Answer: 2.71 1 (approx.), 2.721 (exact).

6. I chose x-increments of 0.2 and calculated the two curves from -2 to +4.
Fortunately the two curves intersected at x = -1 and x = 3. The cells that
were summed to obtain the area are in blue. Area = 10.640.

7. As in the preceding problem, I used x-increments of 0.2. This time it was
necessary to use Goal Seek ... to find the points where the two curves
crossed. After using Goal Seek, the target cell (YI-Y2) was deleted. The
cells that were summed to obtain the area are in blue. Area = 4.822.

8. As in the preceding problem, Goal Seek ... was used to find the two
intersection points. Approximate answer 14900.