use the graph of the function f shown to estimate the following limits and the function value. complete…
use the graph of the function f shown to estimate the following limits and the function value. complete parts (a) through (d). (a) find the limit lim f(x). x→ - 2 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim f(x)= (type an integer or a decimal.) x→ - 2 b. the limit does not exist.
Answer
Explanation:
Step1: Observe the graph as x approaches - 2
Approach x = - 2 from the left - hand side. Look at the y - values the function approaches.
Step2: Determine the limit value
If the function approaches a single y - value as x approaches - 2 from the left, that is the left - hand limit.
Answer:
Since the graph of the function is not provided in a way that we can see the actual y - value as x approaches - 2 from the left, we cannot give a numerical answer. But in general, if the function approaches a single value L as x approaches - 2 from the left, the answer would be A. $\lim_{x\rightarrow - 2^{-}}f(x)=L$ (where L is the value it approaches), and if it approaches different values from different paths as x approaches - 2 from the left or has a break in the graph such that there is no single value it approaches, the answer would be B. The limit does not exist. Without seeing the actual graph, we cannot determine which choice is correct.