$\"\"$

The piecewise function is $\"\\small$ .

Graph :

Graph the piecewise function $\"\\small$ :

$\"\"$

Observe the above graph.

As $\"x\"$ tends to $\"-1\"$ from left side, $\"f(x)\"$ approaches to $\"0\"$ .

So $\"\\lim_{x\\rightarrow-1^-}f(x)=0\"$ .

As $\"x\"$ tends to $\"-1\"$ from right side, $\"f(x)\"$ approaches to $\"1\"$ .

So $\"\\lim_{x\\rightarrow-1^+}f(x)=1\"$ .

Left hand limit and right limits are not equal, $\"\\lim_{x\\rightarrow$ does not exist at $\"x=-1\"$ .

Therefore $\"\\lim_{x\\rightarrow$ exist for all values of $\"a\"$ except $\"a=-1\"$ .

$\"\"$

Graph of the piecewise function $\"\\small$ is

$\"\"$

$\"\\lim_{x\\rightarrow$ exist for all values of $\"a\"$ except $\"a=-1\"$ .