Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §6.4 Logarithms, #76 · Calculus · Differentiation rules

Show that … is satisfied by … and … with

Show that $(ln x) / x = (ln y) / y$ is satisfied by
$x = (\frac{t + 1}{t})^{t}$ and $y = (\frac{t + 1}{t})^{t + 1}$
with $t \neq = 0$ . Graph those points to show the curve $x^{y} = y^{x}$ . It crosses the line $y = x$ at $x =$ ____, where $t \to \infty$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §6.4 Logarithms, #76

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