Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches 2 where f of x equals x plus 3 when x is less than 2 and f of x equals 3 minus x when x is greater than or equal to 2.

1. the limit does not exist.

2. 1

3. 2

4. 5

Option 1.

The limit does not exist.

Step-by-step explanation:

The function is  

We seek to find

Then we must find the limits on the right of 2 () and on the left of 2 ()

If both limits exist and are equal then the exists, if both limits are different or do not exist then the does not exist.  

Limit on the left of 2

Limit on the rigth of 2

Note that both limits give different results. The limit of f(x) when x tends to 2 on the left is equal to 5, and the limit of f(x) when x tends to 2 on the rigth is equal to 1.

Then the does not exist.

The correct option is 1.

Step-by-step explanation:

The given function is

We need to find the .

The limit of a function exist if the left hand limit is equal to the right hand limit.

Left hand limit:

Apply limit.

Right hand limit:

Apply limit.

Since LHL≠RHL, therefore the limit does not exist. Option 1 is correct.