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

Answer:

Lim f(x) does not exist.

Step-by-step 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.