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Question

Answer 1

Step 1:

(5)

Find at .

Observe the graph.

The solid dot represents the value of the function at .

Therefore .

Find .

Left hand limit :

As x tends to from left side, approaches to 4.

.

Right hand limit :

As x tends to from right side, approaches to 4.

.

Left hand limit and right hand limit are equal, so limit exists.

.

Step 2:

(6)

Find at .

Observe the graph.

The solid dot represents the value of the function at .

Therefore .

Find .

Left hand limit :

As x tends to from left side, approaches to 1.

.

Right hand limit :

As x tends to from right side, approaches to .

.

Left hand limit and right hand limit are not equal, so limit does not exists.

does not exist.

Solution :

(5) and .

(6) and does not exist.

Answer 2

Step 1:

(7)

Find at .

Observe the graph.

The solid dot represents the value of the function at .

Therefore .

Find .

Left hand limit :

As x tends to 2 from left side, approaches to .

.

Right hand limit :

As x tends to 2 from right side, approaches to 2.

.

Left hand limit and right hand limit are not equal, so limit does not exists.

does not exist.

Step 2:

(8)

Find at .

Observe the graph.

The solid dot represents the value of the function at .

Therefore .

Find .

Left hand limit :

As x tends to 3 from left side, approaches to 5.

.

Right hand limit :

As x tends to 3 from right side, approaches to 5.

.

Left hand limit and right hand limit are equal, so limit exists.

.

Solution :

(7) and does not exist.

(8) and .