Evaluate limits of the given function

Question

 

Answer 1

Step 1:

The piecewise function is .

If , then .

If , then .

7) The limit is.

Here , So .

.

Step 2:

8) The limit is .

Find the left hand limit and right hand limit at .

Left hand limit:

.

Right hand limit:

.

Since the left and right hand limits are not equal at , limit does not exist.

Therefore, does not exist.

Solution:

7).

8) does not exist.