Question

The slope of the tangent to a curve C : y=y(x) at any point [x, y) on it is $\frac{2 e ^{2 x }-6 e ^{- x }+9}{2+9 e ^{-2 x }}$ If C passes through the points $\left(0, \frac{1}{2}+\frac{\pi}{2 \sqrt{2}}\right)$and \left(\alpha, \frac{1}{2} e ^{2 \alpha}\right)$$ then e ^\alpha$ is equal to :

• A. $\frac{3+\sqrt{2}}{3-\sqrt{2}}$
• B. $\frac{3}{\sqrt{2}}\left(\frac{3+\sqrt{2}}{3-\sqrt{2}}\right)$
• C. $\frac{1}{\sqrt{2}}\left(\frac{\sqrt{2}+1}{\sqrt{2}-1}\right)$
• D. $\frac{\sqrt{2}+1}{\sqrt{2}-1}$

Answer 1

Answer: (B)

$\frac{3}{\sqrt{2}}\left(\frac{3+\sqrt{2}}{3-\sqrt{2}}\right)$

Answer 2

The correct option is(B): $\frac{3}{\sqrt{2}}\left(\frac{3+\sqrt{2}}{3-\sqrt{2}}\right)$.