1 Fig. 1 shows some spreadsheet output concerning the values of a function, \(\mathrm { f } ( x )\).
\begin{table}[h]
| A | B | C | |
| 1 | \(x\) | \(\mathrm { f } ( x )\) | | |
| 2 | 1 | 0.367879441 | 0.367879441 | |
| 3 | 2 | 0.018315639 | 0.38619508 | |
| 4 | 3 | 0.00012341 | 0.38631849 | |
| 5 | 4 | \(1.12535 \mathrm { E } - 07\) | 0.386318602 | |
| 6 | 5 | \(1.38879 \mathrm { E } - 11\) | 0.386318602 | |
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{table}
The formula in cell B2 is ==EXP(-(A2\^{}2)) and equivalent formulae are in cells B3 to B6.
The formula in cell C 2 is \(= \mathrm { B } 2\).
The formula in cell C3 is \(\quad = \mathrm { C } 2 + \mathrm { B } 3\).
Equivalent formulae are in cells C4 to C6.
- Use sigma notation to express the formula in cell C5 in standard mathematical notation.
- Explain why the same value is displayed in cells C 5 and C 6.
Now suppose that the value in cell C2 is chopped to 3 decimal places and used to approximate the value in cell C2.
- Calculate the relative error when this approximation is used.
Suppose that the values in cells B4, B5 and B6 are chopped to 3 decimal places and used as approximations to the original values in cells B4, B5 and B6 respectively.
- Explain why the relative errors in these approximations are all the same.