The area bounded by the parabola $$2y = {x^2}$$ and the lines $$x=y-4$$ is equal to _________.

If $$H(x, y)$$ is homogeneous function of degree $$n$$ then $$x{{\partial H} \over {\partial x}} + y{{\partial H} \over {\partial y}} = nH$$

The value of $$\int\limits_0^\infty {{e^{ - {y^3}}}.{y^{1/2}}} $$ dy is _________.

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