Concept explainers
(a)
To find: The limit of each of the given functions and explain if the limit does not exist.
(a)
Answer to Problem 1RE
(i) The value of
(ii) The value of
(iii) The value of
(iv) The value of
(v) The value of
(vi) The value of
(vii) The value of
(viii) The value of
Explanation of Solution
Calculation:
Section (i)
Obtain the value of
From the given graph, it is found that the curve move towards
Therefore,
Section (ii)
Obtain the value of
From the given graph, it is found that the curve move towards
Therefore,
Section (iii)
Obtain the value of
From section (ii),
From the given graph, it is found that the curve move towards
Thus,
Recall the definition that
Since
Therefore,
Section (iv)
Obtain the value of
From the given graph, it is found that the curve move towards
Therefore,
Section (v)
Obtain the value of
From the given graph, it is found that the curve move towards infinity as x approaches
Therefore,
Section (vi)
Obtain the value of
From the given graph, it is found that the curve move towards negative infinity as x approaches 2 from the left side.
Therefore,
Section (vii)
Obtain the value of
From the given graph, it is found that the curve move towards
Therefore,
Section (viii)
Obtain the value of
From the given graph, it is found that the curve move towards
Therefore,
(b)
To state: The equation of horizontal asymptotes.
(b)
Answer to Problem 1RE
The equation of horizontal asymptotes are
Explanation of Solution
Recall from the definition that
From the previous parts,
Thus, equation of horizontal asymptotes are
(c)
To state: The equation of vertical asymptotes.
(c)
Answer to Problem 1RE
The equation of vertical asymptotes are
Explanation of Solution
Recall from the definition that
From the previous parts,
Thus, equation of vertical asymptotes are
(d)
To find: The numbers at which f is discontinuous.
(d)
Answer to Problem 1RE
f is discontinuous at
Explanation of Solution
From the given graph,
Thus, f is discontinuous at
From the given graph,
Thus, f is discontinuous at
From the given graph,
Thus, f is discontinuous at
From the given graph,
Recall from the definition that f is continuous at
Thus, f is discontinuous at
Therefore, f is discontinuous at
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- 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