Exercise Solution 4.16

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

[s1]

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

[s2]

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

[s3]

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

 

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