### Homework 1.2**Instructions:**Use the given graph of the function $ g $ to find the following limits:**Graph Analysis:**- The graph is provided in a coordinate system with both x-axis and y-axis.- The function $ g(x) $ is plotted with a blue curve.- There are notable points on the graph that may correspond to specific values of $ g(x) $ as $ x $ approaches certain values.**Tasks:**1. $\lim_{{x \to -2}} g(x) = $ - Determine the limit of $ g(x) $ as $ x $ approaches $-2$.2. $\lim_{{x \to 2}} g(x) = $ - Determine the limit of $ g(x) $ as $ x $ approaches 2.3. $\lim_{{x \to -2^+}} g(x) = $ - Determine the limit of $ g(x) $ as $ x $ approaches $-2$ from the right-hand side.4. $\lim_{{x \to 0}} g(x) = $ - Determine the limit of $ g(x) $ as $ x $ approaches 0.5. $ g(2) = $ - Determine the value of $ g(x) $ at $ x = 2 $.To help understand the calculations:- Hover over the graph or use graphing software to visualize the behavior of $ g(x) $ near the specified points.- Notice any discontinuities or holes in the graph to determine if the limits exist and what their values might be.If further help is needed with limits, click on the "help (limits)" link.\[\boxed{\text{help (limits)}}\]*Note: Ensure your answers are as precise as possible to match the graph accurately.*---**Graph Explanation:**- The graph displays $ g(x) $ with distinct portions of the curve indicating behavior near $ x = -2 $, $ x = 2 $, and $ x = 0 $.- Observe vertical and horizontal asymptotes, peaks, troughs, and points of intersection to deduce accurate values for the limits.By examining the graph closely, you should be able to accurately determine each limit and the value of \(

Answered: Image /qna-images/answer/2ec6c4da-2759-4d04-9754-db2c0745b440.jpg

Answered: Use the given graph of the function g…

Use the given graph of the function g to find the following limits: 1e 1. lim g(z) : %3D help (limits) 2. lim g(z) = -12 3. lim g(z) = %3D H+2 4. n g(z) = 5. g(2)

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

### Homework 1.2

**Instructions:**
Use the given graph of the function $ g $ to find the following limits:

**Graph Analysis:**
- The graph is provided in a coordinate system with both x-axis and y-axis.
- The function $ g(x) $ is plotted with a blue curve.
- There are notable points on the graph that may correspond to specific values of $ g(x) $ as $ x $ approaches certain values.

**Tasks:**

1. $\lim_{{x \to -2}} g(x) = $
- Determine the limit of $ g(x) $ as $ x $ approaches $-2$.

2. $\lim_{{x \to 2}} g(x) = $
- Determine the limit of $ g(x) $ as $ x $ approaches 2.

3. $\lim_{{x \to -2^+}} g(x) = $
- Determine the limit of $ g(x) $ as $ x $ approaches $-2$ from the right-hand side.

4. $\lim_{{x \to 0}} g(x) = $
- Determine the limit of $ g(x) $ as $ x $ approaches 0.

5. $ g(2) = $
- Determine the value of $ g(x) $ at $ x = 2 $.

To help understand the calculations:
- Hover over the graph or use graphing software to visualize the behavior of $ g(x) $ near the specified points.
- Notice any discontinuities or holes in the graph to determine if the limits exist and what their values might be.

If further help is needed with limits, click on the "help (limits)" link.

\[
\boxed{\text{help (limits)}}
\]

*Note: Ensure your answers are as precise as possible to match the graph accurately.*

---

**Graph Explanation:**
- The graph displays $ g(x) $ with distinct portions of the curve indicating behavior near $ x = -2 $, $ x = 2 $, and $ x = 0 $.
- Observe vertical and horizontal asymptotes, peaks, troughs, and points of intersection to deduce accurate values for the limits.

By examining the graph closely, you should be able to accurately determine each limit and the value of \(

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