$\"\"$

The function is $\"\\small$ .

Graph :

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

$\"\"$

(a)

Find $\"\\lim_{x\\rightarrow0^-}f(x)\"$ .

Observe the above graph.

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

So $\"\\lim_{x\\rightarrow0^-}f(x)=1\"$ .

$\"\"$

(b)

Find $\"\\small$ .

Observe the above graph.

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

So $\"\\small$ .

$\"\"$

(c)

Find $\"\\small$ .

Left hand limit $\"\\lim_{x\\rightarrow0^-}f(x)=1\"$ .

Right hand limit $\"\\small$ .

Left hand limit and right hand limit are not equal, $\"\\small$ does not exist.

$\"\\small$ does not exist.

$\"\"$

(a) $\"\\lim_{x\\rightarrow0^-}f(x)=1\"$ .

(b) $\"\\small$ .