
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Explain why the function is discontinuous at the given
number a . Sketch the graph of the function.

Transcribed Image Text:if x+ 1
f(x) = { x*
a = 1
1
if x= 1
Expert Solution

arrow_forward
Step 1
The function is given ,
f(x)=(x2-xx2-1 , if x≠11, if x=1) for a=1.
To check the function discontinuity,
The left hand limit is,
limh→0f(1-h)=limh→0(1-h)2-(1-h)(1-h)2-1=limh→0[1+h2-2h-1+h1+h2-2h-1]=limh→0[h2-hh2-2h]=limh→0[h-1h-2]=12
arrow_forward
Step 2
The right hand limit is,
limh→0f(1+h)=limh→0(1+h)2-(1+h)(1+h)2-1=limh→0[1+h2+2h-1-h1+h2+2h-1]=limh→0[h2+hh2+2h]=limh→0[h+1h+2]=12
The function at a=1 ,is f(1)=1.
Thus , the LHL=RHL≅f(1).
Step by stepSolved in 3 steps with 1 images

Knowledge Booster
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 TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning

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