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
![On this educational webpage, we explore the process of calculating limits involving absolute values and division. We are tasked with computing the following limit:
\[
\lim_{{x \to 3^-}} \frac{|4x - 12|}{x - 3}.
\]
This expression implies that we are taking the limit of the function \(\frac{|4x - 12|}{x - 3}\) as \(x\) approaches 3 from the left (denoted by the superscript "-"). The absolute value expression \(|4x - 12|\) needs special attention because it influences how the limit is computed just to the left of \(x = 3\).
In this case, when evaluating \(|4x - 12|\) for \(x\) values just less than 3, the absolute value expression \(|4x - 12|\) becomes \(12 - 4x\).
Given the presence of the absolute value, steps one might follow when computing the limit include:
1. Simplifying \(|4x - 12|\) considering the left-handed limit.
2. Calculating the result after substitution.
The limit computation involves analyzing behaviors of the function close to the point of interest, especially due to the potential discontinuity presented by the absolute value at \(x = 3\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fcadb28-95ed-48d9-9459-731288009526%2F60137e6c-fe2e-4f7f-b3b4-1c921500a4ee%2F9h6vpvo_processed.png&w=3840&q=75)
Transcribed Image Text:On this educational webpage, we explore the process of calculating limits involving absolute values and division. We are tasked with computing the following limit:
\[
\lim_{{x \to 3^-}} \frac{|4x - 12|}{x - 3}.
\]
This expression implies that we are taking the limit of the function \(\frac{|4x - 12|}{x - 3}\) as \(x\) approaches 3 from the left (denoted by the superscript "-"). The absolute value expression \(|4x - 12|\) needs special attention because it influences how the limit is computed just to the left of \(x = 3\).
In this case, when evaluating \(|4x - 12|\) for \(x\) values just less than 3, the absolute value expression \(|4x - 12|\) becomes \(12 - 4x\).
Given the presence of the absolute value, steps one might follow when computing the limit include:
1. Simplifying \(|4x - 12|\) considering the left-handed limit.
2. Calculating the result after substitution.
The limit computation involves analyzing behaviors of the function close to the point of interest, especially due to the potential discontinuity presented by the absolute value at \(x = 3\).
Expert Solution
Step 1
_1.jpg)
Step by step
Solved in 2 steps with 2 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