2 The following spreadsheet printout shows the bisection method being applied to the equation \(\mathrm { f } ( x ) = 0\), where \(\mathrm { f } ( x ) = \mathrm { e } ^ { x } - x ^ { 2 } - 2\). Some values of \(\mathrm { f } ( x )\) are shown in columns B and D.
| A | B | C | D | E | F | G |
| 1 | a | \(\mathrm { f } ( a )\) | b | f(b) | \(( a + b ) / 2\) | \(\mathrm { f } ( ( a + b ) / 2 )\) | mpe |
| 2 | 1 | -0.28172 | 2 | 1.389056 | 1.5 | 0.231689 | 0.5 |
| 3 | 1 | -0.28172 | 1.5 | 0.231689 | 1.25 | -0.072157 | 0.25 |
| 4 | 1.25 | -0.07216 | 1.5 | 0.231689 | 1.375 | 0.064452 | 0.125 |
| 5 | 1.25 | -0.07216 | 1.375 | 0.064452 | 1.3125 | -0.007206 | 0.0625 |
| 6 | 1.3125 | -0.00721 | 1.375 | 0.064452 | 1.34375 | 0.027728 | 0.03125 |
- The formula in cell A 3 is \(= \mathrm { IF } ( \mathrm { F } 2 > 0\), A2, E2). State the purpose of this formula.
- The formula in cell C 3 is \(= \mathrm { IF } ( \mathrm { F } 2 > 0 , \ldots , \ldots )\). What are the missing cell references?
- In which row is the magnitude of the maximum possible error (mpe) less than \(5 \times 10 ^ { - 7 }\) for the first time?