(a)

Find . 

Observe the graph.

As  tends to  from left side,  approaches to .

So . 

(b)

Find . 

Observe the graph.

As tends to from right side, approaches to .

. 

(c)

Find . 

Observe the graph.

Left hand limit : 

As tends to from left side, approaches to .

.

Right hand limit .

As tends to from right side, approaches to .

.

Left hand limit and right hand limit are equal, is exist.

. 

(d) 

Find .

Observe the graph that does not exists.

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

So is undefined.

(e)

Find . 

Observe the graph.

As tends to from left side, approaches to .

So . 

(f)

Find . 

Observe the graph.

As tends to from right side, approaches to .

So . 

(g)

Find . 

Observe the graph.

Left hand limit . 

As tends to from left side, approaches to .

. 

Right hand limit . 

As tends to from right side, approaches to .

.

Left hand limit and right hand limit are not equal, does not exist. 

(h)

Find .

Observe the graph that exists.

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

So . 

(i)

Find . 

Observe the graph.

Left hand limit : 

As tends to from left side, approaches to .

. 

Right hand limit : 

As tends to from right side, approaches to .

. 

Left hand limit and right hand limit are equal, is exist.

. 

(j)

Find .

Observe the graph.

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

So is undefined.

(k)

Find . 

Observe the graph.

As tends to from right side, approaches to .

So . 

(l)

Find . 

Observe the graph.

As tends to from left side, oscillates between to .

So does not exist. 

(a) . 

(b) . 

(c) . 

(d) is undefined. 

(e) . 

(f) . 

(g) does not exist. 

(h) . 

(i) . 

(j) is undefined. 

(k) . 

(l) does not exist.