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

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.