Question #4cf41
1 Answer
(Using the Newton Method (see below)
Explanation:
Newton Method:
We want to find the value of
or, assuming
This is equivalent to finding the root of
The Newton Method tells us to start with some initial guess,
(We've been told to use
and
to developing increasingly better approximations
Since
using the exponent rule for derivatives, we have
Entering all of this into a spread sheet:
It is normal to stop this iteration once the difference between successive approximations is less than 8 digits. (In fact, going beyond the last line displayed here has reached the limits for accuracy in my spreadsheet, so no further improvement is possible).
Note: for this case, if we were doing the calculations by hand, performing the long division would be easier.