One of the eigen vector of the matrix $$A = \left[ {\matrix{ 2 & 2 \cr 1 & 3 \cr } } \right]$$ is

The parabolic are $$y = \sqrt x ,1 \le x \le 2$$ is revolved around the $$x$$-axis. The volume of the solid of revolution is

The function $$y = \left| {2 - 3x} \right|$$

The infinite series $${\,f\left( x \right) = x - {{{x^3}} \over {3!}} + {{{x^5}} \over {5!}} - {{{x^7}} \over {7!}} + - - - \,\,}$$ Converges to