The curve r(t) = (t − tanh t, sech t) is called a tractrix (see Exercise 100 in Section 11.1).

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= 5 ||r' (u)|| du is equal to s(t) = ln(cosht). (a) Show that s(t) = (b) Show that t = g(s) = ln(es + es 1) is an inverse of s(t) and verify that - r(s) = (tanh- ( e-2s) - - e-5, e-) - is an arc length parametrization of the tractrix.