use the given graph of the function g to find the following limits: 1. $lim_{x\rightarrow2^{-}}g(x)=2$ help…

use the given graph of the function g to find the following limits: 1. $lim_{x\rightarrow2^{-}}g(x)=2$ help (limits) 2. $lim_{x\rightarrow2^{+}}g(x)= - 2$ 3. $lim_{x\rightarrow2}g(x)= dne$ 4. $lim_{x\rightarrow0}g(x)= - 2$ 5. $g(2)=1$

use the given graph of the function g to find the following limits: 1. $lim_{x\rightarrow2^{-}}g(x)=2$ help (limits) 2. $lim_{x\rightarrow2^{+}}g(x)= - 2$ 3. $lim_{x\rightarrow2}g(x)= dne$ 4. $lim_{x\rightarrow0}g(x)= - 2$ 5. $g(2)=1$

Answer

Explanation:

Step1: Analyze left - hand limit as x→2

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

Step2: Analyze right - hand limit as x→2

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

Step3: Determine limit as x→2

Since $\lim_{x\rightarrow2^{-}}g(x)\neq\lim_{x\rightarrow2^{+}}g(x)$ (2≠ - 2), the two - sided limit $\lim_{x\rightarrow2}g(x)$ does not exist (dne).

Step4: Analyze limit as x→0

As x approaches 0, we observe the graph near x = 0. The y - value that the function approaches is - 2. So, $\lim_{x\rightarrow0}g(x)=-2$.

Step5: Find g(2)

The value of the function at x = 2 is given by the y - value of the filled - in point at x = 2 on the graph. So, g(2)=1.

Answer:

  1. $\lim_{x\rightarrow2^{-}}g(x)=2$
  2. $\lim_{x\rightarrow2^{+}}g(x)=-2$
  3. $\lim_{x\rightarrow2}g(x)$ dne
  4. $\lim_{x\rightarrow0}g(x)=-2$
  5. g(2)=1