Find the mistake in Limit

Question

Given that and ,

Find the value of

.

Find the mistake in the following “method”

Let

From , we get 4 x – 3 y = 6 (1)

From , we get x + y = 5 (2)

Solving (1) and (2), we get x = 3, y = 2.

Therefore,

The answer is correct but there is a big mistake in the concept of limit.

Can you find it ?

Find the solution below.

The point is :

Although and exist,

the limits may not exist.

The correct way :

(here by given the limits exist)

A small question :

How can you find in the above calculation ?