If the function

$$f(x)= \begin{cases}\frac{1}{|x|}, & |x| \geqslant 2 \\ \mathrm{a} x^2+2 \mathrm{~b}, & |x|<2\end{cases}$$

is differentiable on $$\mathbf{R}$$, then $$48(a+b)$$ is equal to __________.

Let $$f(x)=\sqrt{\lim _\limits{r \rightarrow x}\left\{\frac{2 r^2\left[(f(r))^2-f(x) f(r)\right]}{r^2-x^2}-r^3 e^{\frac{f(r)}{r}}\right\}}$$ be differentiable in $$(-\infty, 0) \cup(0, \infty)$$ and $$f(1)=1$$. Then the value of ea, such that $$f(a)=0$$, is equal to _________.

Let $$[x]$$ be the greatest integer $$\leq x$$. Then the number of points in the interval $$(-2,1)$$, where the function $$f(x)=|[x]|+\sqrt{x-[x]}$$ is discontinuous, is ___________.

Let $$f:( - 2,2) \to R$$ be defined by $$f(x) = \left\{ {\matrix{ {x[x],} & { - 2 < x < 0} \cr {(x - 1)[x],} & {0 \le x \le 2} \cr } } \right.$$ where $$[x]$$ denotes the greatest integer function. If m and n respectively are the number of points in $$( - 2,2)$$ at which $$y = |f(x)|$$ is not continuous and not differentiable, then $$m + n$$ is equal to ____________.