To be handed in by 9/22/98, 12:30 p.m.
Code Newton's method and False Positions. Consider single and double precision
versions of these codes.
Test your codes out on special cases, and convince me that you have used a
sensible stopping criterion. In particular, find all roots of
, 
and 
and check convergence rates
(since you know the exact answers). How should you choose your initial guess(es)?
Now find the roots of 
. Find the first three positive solutions
of the equation x=tan(x). How can you be sure that you have all the right roots?
Estimate convergence rates for these last two functions.