$$\mathop {\lim }\limits_{x \to 0} \left( {{{{e^{5x}} - 1} \over x}} \right)$$ is equal to ________.

The value of $$\mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} {{{x^2} - xy} \over {\sqrt x - \sqrt y }}$$ is

The curve $$\,\,y = {x^4}\,\,$$

A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $$y = 2x\,\,\, - 0.1{x^2}$$ where $$y$$ is the height of the arch in meters. The maximum possible height of the arch is