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 $t \to \infty$ .

~11 minWritten answer · check your work with Lemma

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

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Attach photos of your pages (up to 3) or one PDF — or check what you typed above. Lemma reads the work and verifies the reasoning, not just the answer.

Your first check today doesn't need an account.

Your photos and PDFs are read once and not stored — only the transcription is kept.