Exercise Solution 4.16

The first order Taylor polynomial of a function f of a variable tx about a fixed point x[0] is:


Treating tzlog as the function f, we construct a second order Taylor polynomial about an arbitrary point x[0]:


Substituting the specific point t–1x for x[0], this becomes


which is the formula for simple return. We conclude that tzsimple is the first-order Taylor polynomial for tzlog.