The slope of the tangent to C:y=y(x) at (x,y) is 2e^2x-6e^-x+92+9e^-2x.

Question

The slope of the tangent to $C:y=y(x)$ at $(x,y)$ is $\dfrac{2e^{2x}-6e^{-x}+9}{2+9e^{-2x}}$. If $C$ passes through $\left(0,\dfrac12+\dfrac{\pi}{2\sqrt2}\right)$ and $\left(\alpha,\dfrac12 e^{2\alpha}\right)$, then $e^\alpha$ is:

Accepted Answer

Integrating the given slope and matching the two given points determines $e^\alpha = \dfrac{3}{\sqrt2}\cdot\dfrac{3+\sqrt2}{3-\sqrt2}$.

Solutions · 1