If $$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\sin x} \over x} = l$$ and $$\mathop {\lim }\limits_{x \to \infty } {{\cos x} \over x} = m$$, then which one of the following is correct?

The left-hand derivative of f(x) = [x] sin ($$\pi$$x) at x = k, where k is an integer and [x] is the greatest integer function, is

The set of all points, where the function $$f(x) = \sqrt {1 - {e^{ - {x^2}}}} $$ is differentiable, is

If $$f(x) = x(\sqrt x - \sqrt {x + 1} )$$, then f(x) is