Graphical limits: Use the graph provided below to write a value for each part (if i exists). If the value does not exist, write “DNE”. No need to show work. Part. a. y ਜਾ 2 Part. b. Part. c. lim f(x) x → −5+ f(-2) lim f(x) x-2 1. f(x) |
Graphical limits: Use the graph provided below to write a value for each part (if i exists). If the value does not exist, write “DNE”. No need to show work. Part. a. y ਜਾ 2 Part. b. Part. c. lim f(x) x → −5+ f(-2) lim f(x) x-2 1. f(x) |
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...
Related questions
Question
![**Graphical Limits: Analyzing the Graph**
To understand graphical limits, let's analyze the provided graph to find the required values or identify if they do not exist (DNE). Here is the graph and a detailed step-by-step solution for each part.
### Graph Analysis:
The graph of the function \( f(x) \) is provided, showing various behaviors at critical points:
1. **Discontinuities and Limits:**
- The function \( f(x) \) has vertical asymptotes, holes (open circles), and jump discontinuities (sudden changes in value).
2. **Key Points:**
- The graph approaches certain y-values as \( x \) approaches specific points from the left (\( x^- \)) or right (\( x^+ \)).
- Open and closed circles indicate holes and actual function values, respectively.
### Parts:
**Part a.**
\[ \lim_{{x \to -5^+}} f(x) \]
As \( x \) approaches \(-5\) from the right, the graph tends to \( y = 4 \).
\[ \boxed{4} \]
**Part b.**
\[ f(-2) \]
At \( x = -2 \), \( f(x) \) is indicated by a closed circle at \( y = -3 \).
\[ \boxed{-3} \]
**Part c.**
\[ \lim_{{x \to -2}} f(x) \]
Although \( f(-2) = -3 \), the limits from both directions towards \( x = -2 \) are different, so the limit does not exist.
\[ \boxed{\text{DNE}} \]
**Part d.**
\[ \lim_{{x \to 4^-}} f(x) \]
As \( x \) approaches \( 4 \) from the left, the graph tends to \( y = 2 \).
\[ \boxed{2} \]
**Part e.**
\[ \lim_{{x \to -1}} f(x) \]
As \( x \) approaches \(-1\), the left-hand and right-hand limits do not converge to the same value.
\[ \boxed{\text{DNE}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9a5f5a5-4eae-476c-bcab-4a001ac27552%2Fd7b0defb-4c4f-43ee-9a41-2eb863a87814%2F6jz1o8i_processed.png&w=3840&q=75)
Transcribed Image Text:**Graphical Limits: Analyzing the Graph**
To understand graphical limits, let's analyze the provided graph to find the required values or identify if they do not exist (DNE). Here is the graph and a detailed step-by-step solution for each part.
### Graph Analysis:
The graph of the function \( f(x) \) is provided, showing various behaviors at critical points:
1. **Discontinuities and Limits:**
- The function \( f(x) \) has vertical asymptotes, holes (open circles), and jump discontinuities (sudden changes in value).
2. **Key Points:**
- The graph approaches certain y-values as \( x \) approaches specific points from the left (\( x^- \)) or right (\( x^+ \)).
- Open and closed circles indicate holes and actual function values, respectively.
### Parts:
**Part a.**
\[ \lim_{{x \to -5^+}} f(x) \]
As \( x \) approaches \(-5\) from the right, the graph tends to \( y = 4 \).
\[ \boxed{4} \]
**Part b.**
\[ f(-2) \]
At \( x = -2 \), \( f(x) \) is indicated by a closed circle at \( y = -3 \).
\[ \boxed{-3} \]
**Part c.**
\[ \lim_{{x \to -2}} f(x) \]
Although \( f(-2) = -3 \), the limits from both directions towards \( x = -2 \) are different, so the limit does not exist.
\[ \boxed{\text{DNE}} \]
**Part d.**
\[ \lim_{{x \to 4^-}} f(x) \]
As \( x \) approaches \( 4 \) from the left, the graph tends to \( y = 2 \).
\[ \boxed{2} \]
**Part e.**
\[ \lim_{{x \to -1}} f(x) \]
As \( x \) approaches \(-1\), the left-hand and right-hand limits do not converge to the same value.
\[ \boxed{\text{DNE}} \]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning