(a)

Find $\"\\small$ .

Observe the graph.

Left hand limit $\"\\lim_{x\\rightarrow1^-}f(x)\"$ :

As $\"x\"$ approaches to $\"1\"$ from left side, $\"f(x)\"$ approaches to $\"2\"$ .

$\"\\lim_{x\\rightarrow1^-}f(x)=2\"$ .

Right hand limit $\"\\lim_{x\\rightarrow1^+}f(x)\"$ :

As $\"x\"$ approaches to $\"1\"$ from right side, $\"f(x)\"$ approaches to $\"2\"$ .

$\"\\lim_{x\\rightarrow1^+}f(x)=2\"$ .

Left hand limit and right hand limit are equal, $\"\\small$ is exist.

$\"\\small$ .

(b)

Find $\"\\lim_{x\\rightarrow3^-}f(x)\"$ .

Observe the graph.

As $\"x\"$ tends to $\"3\"$ from left side, $\"f(x)\"$ approaches to $\"1\"$ .

So $\"\\lim_{x\\rightarrow3^-}f(x)=1\"$ .

(c)

Find $\"\\lim_{x\\rightarrow3^+}f(x)\"$ .

Observe the graph.

As $\"x\"$ tends to $\"3\"$ from right side, $\"f(x)\"$ approaches to $\"4\"$ .

So $\"\\lim_{x\\rightarrow3^+}f(x)=4\"$ .

(d)

Find $\"\\small$ .

Observe the graph.

Left hand limit $\"\\lim_{x\\rightarrow3^-}f(x)\"$ :

As $\"x\"$ approaches to $\"3\"$ from left side, $\"f(x)\"$ approaches to $\"1\"$ .

$\"\\lim_{x\\rightarrow3^-}f(x)=1\"$ .

Right hand limit $\"\\lim_{x\\rightarrow3^+}f(x)\"$ :

As $\"x\"$ approaches to $\"3\"$ from right side, $\"f(x)\"$ approaches to $\"4\"$ .

$\"\\lim_{x\\rightarrow3^+}f(x)=4\"$ .

Here left hand limit and right hand limit are not equal.

$\"\\small$ does not exist.

(e)

Find $\"f(3)\"$ .

Observe the graph that $\"f(3)\"$ exists.

The solid dot indicates that value of the function exist at $\"x=3\"$ .

The value of the function at $\"x=3\"$ is $\"3\"$ .

So $\"f(3)=3\"$ .

(a) $\"\\small$ .

(b) $\"\\lim_{x\\rightarrow3^-}f(x)=1\"$ .

(c) $\"\\lim_{x\\rightarrow3^+}f(x)=4\"$ .

(d) $\"\\small$ does not exist.

(e) $\"f(3)=3\"$ .