use the graph to find the following limits and function value for each value of a.\ni) $lim_{x\rightarrow…

use the graph to find the following limits and function value for each value of a.\ni) $lim_{x\rightarrow a^{-}}f(x)$ ii) $lim_{x\rightarrow a^{+}}f(x)$ iii) $lim_{x\rightarrow a}f(x)$ iv) $f(a)$, if it exists.\na. for $a = 1$ b. for $a = 3$\na. i) select the correct choice below and, if necessary, fill in the answer box within your choice.\na. $lim_{x\rightarrow1^{-}}f(x)=square$ (type an integer or a decimal.)\nb. the limit does not exist.\nii) select the correct choice below and, if necessary, fill in the answer box within your choice.\na. $lim_{x\rightarrow1^{+}}f(x)=square$ (type an integer or a decimal.)\nb. the limit does not exist.\niii) select the correct choice below and, if necessary, fill in the answer box within your choice.\na. $lim_{x\rightarrow1}f(x)=square$ (type an integer or a decimal.)\nb. the limit does not exist.\niv) find $f(1)$. choose the correct answer below.

use the graph to find the following limits and function value for each value of a.\ni) $lim_{x\rightarrow a^{-}}f(x)$ ii) $lim_{x\rightarrow a^{+}}f(x)$ iii) $lim_{x\rightarrow a}f(x)$ iv) $f(a)$, if it exists.\na. for $a = 1$ b. for $a = 3$\na. i) select the correct choice below and, if necessary, fill in the answer box within your choice.\na. $lim_{x\rightarrow1^{-}}f(x)=square$ (type an integer or a decimal.)\nb. the limit does not exist.\nii) select the correct choice below and, if necessary, fill in the answer box within your choice.\na. $lim_{x\rightarrow1^{+}}f(x)=square$ (type an integer or a decimal.)\nb. the limit does not exist.\niii) select the correct choice below and, if necessary, fill in the answer box within your choice.\na. $lim_{x\rightarrow1}f(x)=square$ (type an integer or a decimal.)\nb. the limit does not exist.\niv) find $f(1)$. choose the correct answer below.

Answer

Explanation:

Step1: Analyze left - hand limit as x→1⁻

As x approaches 1 from the left side (x→1⁻), we look at the part of the graph to the left of x = 1. Following the curve, the y - value approaches 2. So, $\lim_{x\rightarrow1^{-}}f(x)=2$.

Step2: Analyze right - hand limit as x→1⁺

As x approaches 1 from the right side (x→1⁺), we look at the part of the graph to the right of x = 1. Following the curve, the y - value approaches 2. So, $\lim_{x\rightarrow1^{+}}f(x)=2$.

Step3: Analyze overall limit as x→1

Since $\lim_{x\rightarrow1^{-}}f(x)=\lim_{x\rightarrow1^{+}}f(x) = 2$, then $\lim_{x\rightarrow1}f(x)=2$.

Step4: Find f(1)

Looking at the graph, the solid dot at x = 1 has a y - value of 2. So, f(1)=2.

Answer:

a. i) A. $\lim_{x\rightarrow1^{-}}f(x)=2$ ii) A. $\lim_{x\rightarrow1^{+}}f(x)=2$ iii) A. $\lim_{x\rightarrow1}f(x)=2$ iv) 2