Step 1:

Observe the graph of the function:

We can observe from the graph that  exists.

As tends to from the left hand side, tends to .

As tends to from the right hand side, tends to .

Since the left hand limit and right hand limit are equal,

Step 1:

Observe the graph of the function:

We can observe from the graph that   does not exists.

As tends to from the left hand side, tends to .

As tends to from the right hand side, tends to .

Since the left hand limit and right hand limit are not equal,

does not exist. \ \

Since the left hand limit and right hand limit are not equal,

Limit does not exist at .

does not exist.

(c)

We can observe from the graph that exists.

The solid dot indicates that value of the function exist at .

.

(d)

We can observe from the graph that does not exists.

As tends to  from the left hand side, tends to .

As tends to from the right hand side, tends to .

Since the left hand limit and right hand limit are not equal,

Limit does not exist at .

does not exist.

(e)

We can observe from the graph that does not exists.

The hollow dot indicates that value of the function does not exist at .

is undefined.

(f)

We can observe from the graph that exists.

As tends to  from the left hand side, tends to .

As tends to from the right hand side, tends to .

Since the left hand limit and right hand limit are equal,

Limit exist at .

.

(g)

We can observe from the graph that exists.

The solid dot indicates that value of the function exist at .

.

(h)

As tends to 4 from the left hand side, tends to .

As tends to 4 from the right hand side, tends to .

Since the left hand limit and right hand limit are undefined,

Limit does not exist at .

does not exist.

(a) is undefined.

(b) does not exist.

(c) .

(d)  does not exist.

(e) is undefined.

(f) .

(g) .

(h) does not exist.