If $$\,\,\,y = x + \sqrt {x + \sqrt {x + \sqrt {x + .....\alpha } } } \,\,\,$$ then $$y(2)=$$ __________.

$$\mathop {Lim}\limits_{x \to 0} {{{e^x} - \left( {1 + x + {{{x^2}} \over 2}} \right)} \over {{x^3}}} = $$

By a change of variables $$x(u, v) = uv,$$ $$\,\,y\left( {u,v} \right) = {v \over u}$$ in a double integral, the integral $$f(x, y)$$ changes to $$\,\,\,f\left( {uv,{\raise0.5ex\hbox{$\scriptstyle v$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle u$}}} \right).\,\,\,$$ Then $$\,\,\phi \left( {u,v} \right)\,\,\,$$ is ________.

The volume of an object expressed in spherical co-ordinates is given by
$$V = \int\limits_0^{2\pi } {\int\limits_0^{{\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 3$}}} {\int\limits_0^1 {{r^2}} \,Sin\phi \,drd\phi \,d\theta .} } $$ The value of the integral