The function $$f\left( x \right) = {x^2} = x + x + x + ....x$$ times, is defined

$$\,\mathop {Lim}\limits_{x \to 0} \left( {{{1 - \cos x} \over {{x^2}}}} \right)$$ is

At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has

The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is