Homework Help is Here – Start Your Trial Now!
Math
Calculus
3. 2- 2. 1 2. (a) lim f(x)= (b) lim f(x)= x-1- (c) lim f(x) = x- 2 (d) lim f(x) = x- -1+

3. 2- 2. 1 2. (a) lim f(x)= (b) lim f(x)= x-1- (c) lim f(x) = x- 2 (d) lim f(x) = x- -1+

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
### Understanding Limits from a Graph #### Instruction: The image contains a graph of a function \( f(x) \) along with a set of questions geared towards evaluating the limits of this function at specific points. Below is a detailed explanation of the graph and each question. #### Graph Description: The graph presents a function \( f(x) \) plotted over an interval. Key points of interest on the graph are: - An open circle at \( (2, 0) \), indicating that the function is not defined at \( x = 2 \). - The graph shows a vertical asymptote approaching \( x = 1 \). - The function decreases to negative infinity as it approaches \( x = 1 \) from the left and increases to positive infinity as it approaches \( x = 1 \) from the right. #### Questions and Required Answers: (a) \(\lim_{{x \to 1^-}} f(x) =\) Interpretation: This asks for the limit of \( f(x) \) as \( x \) approaches 1 from the left side (denoted \( 1^- \)). - Observation from graph: As \( x \) approaches 1 from the left, \( f(x) \) heads towards negative infinity. - **Answer:** \(-\infty\) (b) \(\lim_{{x \to 1^+}} f(x) =\) Interpretation: This asks for the limit of \( f(x) \) as \( x \) approaches 1 from the right side (denoted \( 1^+ \)). - Observation from graph: As \( x \) approaches 1 from the right, \( f(x) \) heads towards positive infinity. - **Answer:** \(+\infty\) (c) \(\lim_{{x \to 1}} f(x) =\) Interpretation: This asks for the overall limit of \( f(x) \) as \( x \) approaches 1 from both sides. - Observation from graph: Since the left limit \((x \to 1^-)\) and the right limit \((x \to 1^+)\) are different, the overall limit does not exist. - **Answer:** Does not exist (d) \(\lim_{{x \to 2^-}} f(x) =\) Interpretation: This asks for the limit of \( f(x) \) as
Transcribed Image Text:### Understanding Limits from a Graph #### Instruction: The image contains a graph of a function \( f(x) \) along with a set of questions geared towards evaluating the limits of this function at specific points. Below is a detailed explanation of the graph and each question. #### Graph Description: The graph presents a function \( f(x) \) plotted over an interval. Key points of interest on the graph are: - An open circle at \( (2, 0) \), indicating that the function is not defined at \( x = 2 \). - The graph shows a vertical asymptote approaching \( x = 1 \). - The function decreases to negative infinity as it approaches \( x = 1 \) from the left and increases to positive infinity as it approaches \( x = 1 \) from the right. #### Questions and Required Answers: (a) \(\lim_{{x \to 1^-}} f(x) =\) Interpretation: This asks for the limit of \( f(x) \) as \( x \) approaches 1 from the left side (denoted \( 1^- \)). - Observation from graph: As \( x \) approaches 1 from the left, \( f(x) \) heads towards negative infinity. - **Answer:** \(-\infty\) (b) \(\lim_{{x \to 1^+}} f(x) =\) Interpretation: This asks for the limit of \( f(x) \) as \( x \) approaches 1 from the right side (denoted \( 1^+ \)). - Observation from graph: As \( x \) approaches 1 from the right, \( f(x) \) heads towards positive infinity. - **Answer:** \(+\infty\) (c) \(\lim_{{x \to 1}} f(x) =\) Interpretation: This asks for the overall limit of \( f(x) \) as \( x \) approaches 1 from both sides. - Observation from graph: Since the left limit \((x \to 1^-)\) and the right limit \((x \to 1^+)\) are different, the overall limit does not exist. - **Answer:** Does not exist (d) \(\lim_{{x \to 2^-}} f(x) =\) Interpretation: This asks for the limit of \( f(x) \) as
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Limits and Continuity
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS