Homework Help is Here – Start Your Trial Now!
Math
Calculus
x lim f(x)= x-5- lim f(x)= 2-5+ lim f(x) = 2-5 4 -11 4.9 -13.7 4.99 5 5.01 5.1 -13.97 -9 -14.03 -14.3 6 -17

x lim f(x)= x-5- lim f(x)= 2-5+ lim f(x) = 2-5 4 -11 4.9 -13.7 4.99 5 5.01 5.1 -13.97 -9 -14.03 -14.3 6 -17

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
Answer all8
## Evaluating Limits Using a Table To evaluate the limits of a function \( f(x) \) as \( x \) approaches a certain value, we can use the values provided in a table. Below is a table and three limit expressions that need to be evaluated. ### Table of Values: | \( x \) | 4 | 4.9 | 4.99 | 5 | 5.01 | 5.1 | 6 | |-------------|-------|--------|--------|-------|--------|-------|-------| | \( f(x) \) | -11 | -13.7 | -13.97| -9 | -14.03| -14.3 | -17 | ### Limits to Evaluate: 1. \( \lim_{{x \to 5^-}} f(x) = \) 2. \( \lim_{{x \to 5^+}} f(x) = \) 3. \( \lim_{{x \to 5}} f(x) = \) #### Analysis: 1. **Left-hand limit (\( \lim_{{x \to 5^-}} f(x) \))**: - As \( x \) approaches 5 from the left (\( 4, 4.9, 4.99 \)), \( f(x) \) takes the values \(-11, -13.7, -13.97 \). 2. **Right-hand limit (\( \lim_{{x \to 5^+}} f(x) \))**: - As \( x \) approaches 5 from the right (\( 5.01, 5.1, 6 \)), \( f(x) \) takes the values \(-14.03, -14.3, -17 \). 3. **Two-sided limit (\( \lim_{{x \to 5}} f(x) \))**: - For the two-sided limit to exist, the left-hand and right-hand limits must be equal. ### Using the Table for Evaluation: 1. **Left-hand limit (\( \lim_{{x \to 5^-}} f(x) \))**: - Evaluate the trends from the left-hand side values: \( -11 \to -13.7 \to -13.97 \). 2.
Transcribed Image Text:## Evaluating Limits Using a Table To evaluate the limits of a function \( f(x) \) as \( x \) approaches a certain value, we can use the values provided in a table. Below is a table and three limit expressions that need to be evaluated. ### Table of Values: | \( x \) | 4 | 4.9 | 4.99 | 5 | 5.01 | 5.1 | 6 | |-------------|-------|--------|--------|-------|--------|-------|-------| | \( f(x) \) | -11 | -13.7 | -13.97| -9 | -14.03| -14.3 | -17 | ### Limits to Evaluate: 1. \( \lim_{{x \to 5^-}} f(x) = \) 2. \( \lim_{{x \to 5^+}} f(x) = \) 3. \( \lim_{{x \to 5}} f(x) = \) #### Analysis: 1. **Left-hand limit (\( \lim_{{x \to 5^-}} f(x) \))**: - As \( x \) approaches 5 from the left (\( 4, 4.9, 4.99 \)), \( f(x) \) takes the values \(-11, -13.7, -13.97 \). 2. **Right-hand limit (\( \lim_{{x \to 5^+}} f(x) \))**: - As \( x \) approaches 5 from the right (\( 5.01, 5.1, 6 \)), \( f(x) \) takes the values \(-14.03, -14.3, -17 \). 3. **Two-sided limit (\( \lim_{{x \to 5}} f(x) \))**: - For the two-sided limit to exist, the left-hand and right-hand limits must be equal. ### Using the Table for Evaluation: 1. **Left-hand limit (\( \lim_{{x \to 5^-}} f(x) \))**: - Evaluate the trends from the left-hand side values: \( -11 \to -13.7 \to -13.97 \). 2.
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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