But we can't slud the sigmoids because f is periodic. Hence f is odd all of R.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Friday, July 29, 2016 9:14 AM To: math-fun Subject: Re: [math-fun] True or False, Log[Tan[t + p/4]]
I like this proof method best of all.
But there needs a workaround of the usual proof that the antiderivatives of 2 sec(2x) all differ by just a constant.
That does not hold in this case, since each sigmoid of the original function can be slud up or down by an arbitrary amount.
—Dan
----- f(x) = log(tan(x + pi/4)) f(0) = 0 and f'(x) = 2 sec(2x) is even, hence f(x) is odd. -----
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