Question

PLEASE HELPPPPP

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

Answer 1

Lim f(x) does not exist.

Explanation:

First we write the function f(x)

f(x) is a piecewise function

`f(x) = x + 3` if
`x <-4`

`f(x) = 3-x`, if
`x\geq -4`.

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
`x <-4`.

Therefore,
`f(x) = x + 3`

So

`\lim_(x \to -4^-)x + 3 = (-4) +3 = -1`. (Look at the graph)

Limit to the right of -4.

As x approaches -4 on the right then
`x> -4`.

So
`f(x) = 3-x`

Then

`\lim_(x\to -4^+)3-x = 3 - (-4) = 7`. (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.