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 $lim_{x\rightarrow2^{-}}f(x)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x\rightarrow2^{-}}f(x)=square$ (type an integer.) b. the limit does not exist. (b) find $lim_{x\rightarrow2^{+}}f(x)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x\rightarrow2^{+}}f(x)=square$ (type an integer.) b. the limit does not exist. (c) find $lim_{x\rightarrow2}f(x)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x\rightarrow2}f(x)=square$ (type an integer.) b. the limit does not exist. (d) find the function value $f(2)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $f(2)=square$ (type an integer.) b. the function is not defined at $x = 2$

use the graph of the function f shown to estimate the following limits and the function value. complete parts (a) through (d). (a) find $lim_{x\rightarrow2^{-}}f(x)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x\rightarrow2^{-}}f(x)=square$ (type an integer.) b. the limit does not exist. (b) find $lim_{x\rightarrow2^{+}}f(x)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x\rightarrow2^{+}}f(x)=square$ (type an integer.) b. the limit does not exist. (c) find $lim_{x\rightarrow2}f(x)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x\rightarrow2}f(x)=square$ (type an integer.) b. the limit does not exist. (d) find the function value $f(2)$. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $f(2)=square$ (type an integer.) b. the function is not defined at $x = 2$

Answer

Explanation:

Step1: Analyze left - hand limit as x→2⁻

As x approaches 2 from the left (x→2⁻), we look at the part of the graph to the left of x = 2. The y - value approaches 2. So, $\lim_{x\rightarrow2^{-}}f(x)=2$.

Step2: Analyze right - hand limit as x→2⁺

As x approaches 2 from the right (x→2⁺), we look at the part of the graph to the right of x = 2. The y - value approaches 1. So, $\lim_{x\rightarrow2^{+}}f(x)=1$.

Step3: Analyze overall limit as x→2

Since $\lim_{x\rightarrow2^{-}}f(x)=2$ and $\lim_{x\rightarrow2^{+}}f(x)=1$, and the left - hand limit is not equal to the right - hand limit, $\lim_{x\rightarrow2}f(x)$ does not exist.

Step4: Analyze function value at x = 2

There is an open - circle at x = 2 on the graph, which means the function is not defined at x = 2.

Answer:

(A) A. $\lim_{x\rightarrow2^{-}}f(x)=2$ (B) A. $\lim_{x\rightarrow2^{+}}f(x)=1$ (C) B. The limit does not exist. (D) B. The function is not defined at x = 2.