*27*

*Numerical methods*

**27.1***Use an iteration procedure to find the root of the equation* 40*x* = exp *x* *to four significant figures*.

To provide a satisfactory iteration scheme, the equation must be rearranged in the form *x* = *f*(*x*), where *f*(*x*) is a slowly varying function of *x*; we then use *x*_{n+1} = *f*(*x*_{n}) as the iteration scheme.

In the present case the rearrangement is straightforward, as, by taking logarithms, we can write the equation as *x* = ln 40*x*. Since ...

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