MathematicsHard38×since 2002Q3546The slope of the tangent to a curve C:y=y(x)C: y=y(x)C:y=y(x) at any point (x,y)(x, y)(x,y) on it is 2e2x−6e−x+92+9e−2x\frac{2 \mathrm{e}^{2 x}-6 \mathrm{e}^{-x}+9}{2+9 \mathrm{e}^{-2 x}}2+9e−2x2e2x−6e−x+9. If CCC passes through the points (0,12+π22)\left(0, \frac{1}{2}+\frac{\pi}{2 \sqrt{2}}\right)(0,21+22π) and (α,12e2α)\left(\alpha, \frac{1}{2} \mathrm{e}^{2 \alpha}\right)(α,21e2α), then eα\mathrm{e}^{\alpha}eα is equal to :A3+23−2\frac{3+\sqrt{2}}{3-\sqrt{2}}3−23+2B32(3+23−2)\frac{3}{\sqrt{2}}\left(\frac{3+\sqrt{2}}{3-\sqrt{2}}\right)23(3−23+2)C12(2+12−1)\frac{1}{\sqrt{2}}\left(\frac{\sqrt{2}+1}{\sqrt{2}-1}\right)21(2−12+1)D2+12−1\frac{\sqrt{2}+1}{\sqrt{2}-1}2−12+1Check answerSkip