10* Suppose ECR is separated by a pair of relative open subsets U, V Define a function on E as following: f(x)=(-1, x EV EU Show that is continuous on E; that is, for any a € E, given any > 0, there is 8 >0 such that x € (a-8,a+8) nElf(x)-f(a)|

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 4CR
icon
Related questions
Question
please write down your answer in detail.
 
10* Suppose ECR is separated
by a pair of relative open subsets U, V Define a function on E as
following: f(x) =
(1, X EU
-1, x EV
Show that is continuous on E; that is, for any a E E, given any >
0, there is 8 >0 such that x E (a-8, a +8) nElf(x)-f(a)| <e. Hint: Apply 8.27 Remark.
Transcribed Image Text:10* Suppose ECR is separated by a pair of relative open subsets U, V Define a function on E as following: f(x) = (1, X EU -1, x EV Show that is continuous on E; that is, for any a E E, given any > 0, there is 8 >0 such that x E (a-8, a +8) nElf(x)-f(a)| <e. Hint: Apply 8.27 Remark.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage