Can someone explain this question?

The limit does not exist

Step-by-step explanation:

lim as we approach from below 7

x+5 when x=7  

7+5

12

lim as we approach from above 7

5x-25 when x=7  

5*7 -25

35-25

10

The limit does not exist since these numbers are not the same

Limit (left hand side limit) is 12

Limit (right hand side limit) is 10

Limit at 7 DOES NOT EXIST

Step-by-step explanation:

Limit :

When we want to find limit of left side of 7, we take the first part of the function shown (since its defined for ).

We check values very close to 7 but less than it:

So the limit is approaching 12.

Thus, left hand side limit is 12.

Limit :

When we want to find limit of right side of 7, we take the second part of the function shown (since its defined for ).

We check values very close to 7 but greater than it:

So the limit is approaching 10.

Thus, right hand side limit is 10.

Limit at 7:

If both right hand side limit and left hand side limit equal, then the limit at that specific number exists and is equal to it.

Since we see that the left hand limit (12) and the right hand limit (10) ARE NOT EQUAL, so we conclude that the limit at 7 for the function given DOES NOT EXIST.

the 4th choice is the correct one

step-by-step explanation: