$\"\"$

(a)

Find $\"\\lim_{x\\rightarrow-3^-}h(x)\"$ .

Observe the graph.

As $\"x\"$ tends to $\"-3\"$ from left side, $\"h(x)\"$ approaches to $\"4\"$ .

So $\"\\lim_{x\\rightarrow-3^-}h(x)=4\"$ .

$\"\"$

(b)

Find $\"\\lim_{x\\rightarrow-3^+}h(x)\"$ .

Observe the graph.

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

$\"\\lim_{x\\rightarrow-3^+}h(x)=4\"$ .

$\"\"$

(c)

Find $\"\\lim_{x\\rightarrow-3}h(x)\"$ .

Observe the graph.

Left hand limit $\"\\lim_{x\\rightarrow-3^-}h(x)\"$ :

As $\"x\"$ tends to $\"-3\"$ from left side, $\"h(x)\"$ approaches to $\"4\"$ .

$\"\\lim_{x\\rightarrow-3^-}h(x)=4\"$ .

Right hand limit $\"\\lim_{x\\rightarrow-3^+}h(x)\"$ .

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

$\"\\lim_{x\\rightarrow-3^+}h(x)=4\"$ .

Left hand limit and right hand limit are equal, $\"\\lim_{x\\rightarrow-3}h(x)\"$ is exist.

$\"\\lim_{x\\rightarrow-3}h(x)=4\"$ .

$\"\"$

(d)

Find $\"h(-3)\"$ .

Observe the graph that $\"h(-3)\"$ does not exists.

The hallow dot indicates that value of the function does not exist at $\"\\small$ .

So $\"h(-3)\"$ is undefined.

$\"\"$

(e)

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

Observe the graph.

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

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

$\"\"$

(f)

Find $\"\\lim_{x\\rightarrow0^+}h(x)\"$ .

Observe the graph.

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

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

$\"\"$

(g)

Find $\"\\lim_{x\\rightarrow0}h(x)\"$ .

Observe the graph.

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

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

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

Right hand limit $\"\\lim_{x\\rightarrow0^+}h(x)\"$ .

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

$\"\\lim_{x\\rightarrow0^+}h(x)=-1\"$ .

Left hand limit and right hand limit are not equal, $\"\\lim_{x\\rightarrow0}h(x)\"$ does not exist.

$\"\"$

(h)

Find $\"h(0)\"$ .

Observe the graph that $\"h(0)\"$ exists.

The solid dot indicates that value of the function exist at $\"x=0\"$ .

So $\"h(0)=1\"$ .

$\"\"$

(i)

Find $\"\\lim_{x\\rightarrow2}h(x)\"$ .

Observe the graph.

Left hand limit $\"\\lim_{x\\rightarrow2^-}h(x)\"$ :

As $\"x\"$ tends to $\"2\"$ from left side, $\"h(x)\"$ approaches to $\"2\"$ .

$\"\\lim_{x\\rightarrow2^-}h(x)=2\"$ .

Right hand limit $\"\\lim_{x\\rightarrow2^+}h(x)\"$ :

As $\"x\"$ tends to $\"2\"$ from right side, $\"h(x)\"$ approaches to $\"2\"$ .

$\"\\lim_{x\\rightarrow2^+}h(x)=2\"$ .

Left hand limit and right hand limit are equal, $\"\\lim_{x\\rightarrow2}h(x)\"$ is exist.

$\"\\lim_{x\\rightarrow2}h(x)=2\"$ .

$\"\"$

(j)

Find $\"h(2)\"$ .

Observe the graph.

The hallow dot indicates that value of the function does not exist at $\"x=2\"$ .

So $\"h(2)\"$ is undefined.

$\"\"$

(k)

Find $\"\\lim_{x\\rightarrow5^+}h(x)\"$ .

Observe the graph.

As $\"x\"$ tends to $\"5\"$ from right side, $\"h(x)\"$ approaches to $\"3\"$ .

So $\"\\lim_{x\\rightarrow5^+}h(x)=3\"$ .

$\"\"$

(l)

Find $\"\\lim_{x\\rightarrow5^-}h(x)\"$ .

Observe the graph.

As $\"x\"$ tends to $\"5\"$ from left side, $\"h(x)\"$ oscillates between $\"2\"$ to $\"4\"$ .

So $\"\\lim_{x\\rightarrow5^-}h(x)\"$ does not exist.

$\"\"$

(a) $\"\\lim_{x\\rightarrow-3^-}h(x)=4\"$ .

(b) $\"\\lim_{x\\rightarrow-3^+}h(x)=4\"$ .

(c) $\"\\lim_{x\\rightarrow-3}h(x)=4\"$ .

(d) $\"h(-3)\"$ is undefined.

(e) $\"\\lim_{x\\rightarrow0^-}h(x)=1\"$ .

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

(g) $\"\\lim_{x\\rightarrow0}h(x)\"$ does not exist.

(h) $\"h(0)=1\"$ .

(i) $\"\\lim_{x\\rightarrow2}h(x)=2\"$ .

(j) $\"h(2)\"$ is undefined.

(k) $\"\\lim_{x\\rightarrow5^+}h(x)=3\"$ .

(l) $\"\\lim_{x\\rightarrow5^-}h(x)\"$ does not exist.