(d) Consider the set [1, √5] C [−1, √10]. Explain f is not continuous by connectedness, compactness, the Intermediate Value Theorem.
(d) Consider the set [1, √5] C [−1, √10]. Explain f is not continuous by connectedness, compactness, the Intermediate Value Theorem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
d
![Consider the function f : [-1, √10] → R defined by
-G
I,
f(x)
10
8
6
4
2
compactness,
0
f(x) =
0
[x², x > 2;
x ≤ 2.
1
x
Answer each of the following questions on the discontinuity of f.
Compute and compare lim 2+ f(x) and lim-2- f(x).
2
By using the ed definition, explain why lime-2 f(x) does not exist.
2
3
Consider the set (0,5). Find the preimage f-¹((0,5)) and use the topological
characterization of continuous functions.
the Intermediate Value Theorem.
(d) Consider the set [1, √5] C [-1, √10]. Explain f is not continuous by
connectedness,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fbbe91e-b101-441b-b5fc-9477065585b8%2Fa80d02f1-3099-436d-8850-cc60ed3fb1e4%2Fsb7t3k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the function f : [-1, √10] → R defined by
-G
I,
f(x)
10
8
6
4
2
compactness,
0
f(x) =
0
[x², x > 2;
x ≤ 2.
1
x
Answer each of the following questions on the discontinuity of f.
Compute and compare lim 2+ f(x) and lim-2- f(x).
2
By using the ed definition, explain why lime-2 f(x) does not exist.
2
3
Consider the set (0,5). Find the preimage f-¹((0,5)) and use the topological
characterization of continuous functions.
the Intermediate Value Theorem.
(d) Consider the set [1, √5] C [-1, √10]. Explain f is not continuous by
connectedness,
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