MATH SOLVE

3 months ago

Q:
# 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

Accepted Solution

A:

Answer:Lim f(x) does not exist.Step-by-step explanation:First we write the function f(x)
f(x) is a piecewise function
[tex]f(x) = x + 3[/tex] if [tex]x <-4[/tex][tex]f(x) = 3-x[/tex], if [tex]x\geq -4[/tex].
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 [tex]x <-4[/tex].
Therefore, [tex]f(x) = x + 3[/tex]
So
[tex]\lim_{x \to -4^-}x + 3 = (-4) +3 = -1[/tex]. (Look at the graph)
Limit to the right of -4.
As x approaches -4 on the right then [tex]x> -4[/tex].
So [tex]f(x) = 3-x[/tex]Then
[tex]\lim_{x\to -4^+}3-x = 3 - (-4) = 7[/tex]. (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.