Consider the following for the next items that follow:

Let $f(x)=\sqrt{2-x}+\sqrt{2+x}$.

What is the greatest value of the function?

Consider the following for the next items that follow:

Let f(x) = |x| and g(x) = [x] - 1, where [.] is the greatest integer function.

Let $ h(x)=\frac{f(g(x))}{g(f(x))}$.

What is $\displaystyle \lim _{x \rightarrow 0+}$ h(x) equal to ?

Consider the following for the next items that follow:

Let f(x) = |x| and g(x) = [x] - 1, where [.] is the greatest integer function.

Let $ h(x)=\frac{f(g(x))}{g(f(x))}$.

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

Consider the following for the next items that follow:

Let $f(x)= \begin{cases}\frac{x-3}{|x-3|}+a ; & x<3 \\ a-b ; & x=3 \\ \frac{x-3}{|x-3|}+b ; & x>3\end{cases}$ and f(x) be continuous at x = 3.

What is the value of a ?