Let a R and set Question 1 fa: RR: x x +1|-2|2-x+ a. S(a)= {ER: fa(x)=0}. (So, S(a) is a set). P= {a e R: S(a) = 0}. Qa{a ER: fa(x) >0}. = (a) Give S(-4) and S(9). (b) Give P and Q22. (c) Give min(Q2), max(Q2), inf(Q2), and sup(Q2), if they exist.
Let a R and set Question 1 fa: RR: x x +1|-2|2-x+ a. S(a)= {ER: fa(x)=0}. (So, S(a) is a set). P= {a e R: S(a) = 0}. Qa{a ER: fa(x) >0}. = (a) Give S(-4) and S(9). (b) Give P and Q22. (c) Give min(Q2), max(Q2), inf(Q2), and sup(Q2), if they exist.
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
Please help with question 1
![Let a R and set
Question 1
fa: RR: →|x+1|-2|2x|+a.
S(a)= {x R: fa(x)=0}. (So, S(a) is a set).
P= {a R: S(a) = 0}.
Qa= {xER: fa(x) >0}.
(a) Give S(-4) and S(9).
(b) Give P and 22.
(c) Give min(Q2), max(Q2), inf(Q2), and sup(Q2), if they exist.
Question 2
For each of the following sets S, give numbers a R and r> 0, if applicable, such that
S = B(a, r).
(a) S = (-5, 10) [4, 12)
Let meN and set
(-1)m
(b) S (0, 3) U {1,2,6,7}
=
(c) S = [[-7,0] U (4,9]] U [3,6)
Question 3
max {2-(-1)", 3-(-1)+¹}
Am = 7+
m
Bm 2 min {5-m(-1)m+3, 7}
R = {m EN: Bm = -4m}, V = {m EN: Bm = -8}, W = {m EN: Bm = 1}.
(a) Give according to the values of m, expressions for Am and Bm not involving the max or
min operators.
(b) Give explicitly the sets R, V, and W.
Question 4
Let p R, and > 0. Using Thm 1.24, show that B(p, e) nQ contains at least two elements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c044b69-454e-4f9e-8cd6-567ae6231ec2%2F6ae965e0-83b2-4572-ae01-c56ef4c0c461%2Fe2b95o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let a R and set
Question 1
fa: RR: →|x+1|-2|2x|+a.
S(a)= {x R: fa(x)=0}. (So, S(a) is a set).
P= {a R: S(a) = 0}.
Qa= {xER: fa(x) >0}.
(a) Give S(-4) and S(9).
(b) Give P and 22.
(c) Give min(Q2), max(Q2), inf(Q2), and sup(Q2), if they exist.
Question 2
For each of the following sets S, give numbers a R and r> 0, if applicable, such that
S = B(a, r).
(a) S = (-5, 10) [4, 12)
Let meN and set
(-1)m
(b) S (0, 3) U {1,2,6,7}
=
(c) S = [[-7,0] U (4,9]] U [3,6)
Question 3
max {2-(-1)", 3-(-1)+¹}
Am = 7+
m
Bm 2 min {5-m(-1)m+3, 7}
R = {m EN: Bm = -4m}, V = {m EN: Bm = -8}, W = {m EN: Bm = 1}.
(a) Give according to the values of m, expressions for Am and Bm not involving the max or
min operators.
(b) Give explicitly the sets R, V, and W.
Question 4
Let p R, and > 0. Using Thm 1.24, show that B(p, e) nQ contains at least two elements.
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