For the following two (02) items:
Let
$f(x)=\begin{cases}\frac{1-\cos 2x}{x^{2}}&,x<0\\ 9&,x=0\\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4}&,x>0\end{cases}$

What is $\lim _{x\rightarrow 0^{-}}f(x)$ equal to?

For the following three (03) items:
Consider the function f(x) = x|x|

What is $\lim _{x\rightarrow -1}f(x)$ equal to?

For the following three (03) items:
Consider the function f(x) = x|x|

What is the area bounded by the curve f(x) the x-axis and the lines x = - 2 and x = 1

For the following three (03) items:
Consider the function f(x) = x|x|

Consider the following statements:

I. The function is increasing in the interval (-∞,∞),

II. The function is differentiable at x = 0

Which of the statements given above is/are correct?