find the indicated limit, if it exists. limit of f of x as x approaches negative 4 where f of x equals x plus 3 when x is less than negative 4 and f of x equals 3 minus x when x is greater than or equal to negative 4

Lim f(x) does not exist.

Step-by-step explanation:

First we write the function f(x)

f(x) is a piecewise function

  if  

,    if    .

The graph of this function is shown below.

Then we must find the limit when x approaches -4.

We must calculate the limit on the left of -4 and then calculate the limit on the right of -4.

Limit on the left of -4.

As x approaches -4 on the left then .

Therefore,

So

. (Look at the graph)

Limit to the right of -4.

As x approaches -4 on the right then .

So  

Then

. (Look at the graph)

Note that the limit on the left is different from the limit on the right. Then you can conclude that

Lim f(x) does not exist.

146%

step-by-step explanation: