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(1) Prove that the funetion f(r) =! is not uniformly continuous on (0, 1). (Hint: find two sequences {zn}neN and {zm}n€N such that |rn – žnl < but [f(zn) – S(zn)| 2 1 for all n.)

(1) Prove that the funetion f(r) =! is not uniformly continuous on (0, 1). (Hint: find two sequences {zn}neN and {zm}n€N such that |rn – žnl < but [f(zn) – S(zn)| 2 1 for all n.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help with these three questions: this is for my Analysis class.

Safari File Edit View History Bookmarks Window Help Mon Apr 25 11:30 PM h + 88 00 iu.instructure.com U HW 12 U hw12-M413.pdf: SP22: INTRO... Google Docs b Home | bartleby G how to take a screenshot on a... = SP22-NW-MATH-M413-28651 > Files > hw12-M413.pdf @ HTTP Spring 2022 Learn more about hw12-M413.pdf your Ca...00 series Account Home Download hw12-M413.pdf (98.8 KB) Announcements APR 25 Dashboard ZOOM Syllabus HS TRANSCRIPTS HW 12 Pages Courses Assignments (1) Prove that the function f(x) = 1 is not uniformly continuous on (0, 1]. (Hint: find two sequences {an}nɛN and {zn}n€N such that |an – Zn|< but |f(xn) – f(zn)| 2 1 for all n.) TXT Groups Grades 1 text (2) Prove that the function f(x) = Vr is uniformly continuous on [-1,0). (Hint: follow the example of f(x) = V from class, but considering the sets [-1,1] and [1/2, 0) ) stv People Calendar (3) Prove that the piece-wise function defined by Student Engagement Roster (Student) 1 3x - - if x < -2 Inbox Course f(x) = Relocated Items 11 if x = -2 Quiz 12 2 Questionnaire x2 + 5x + if x > -2 History Circleln is integrable on (-4, 7]. (Hint: do not use upper and lower sums, use a theorem) w Circleln (Faculty) TXT P Help text 2 Quiz 11 Page 2 of 2 696 words English (United States) Focus + 160%
Transcribed Image Text:Safari File Edit View History Bookmarks Window Help Mon Apr 25 11:30 PM h + 88 00 iu.instructure.com U HW 12 U hw12-M413.pdf: SP22: INTRO... Google Docs b Home | bartleby G how to take a screenshot on a... = SP22-NW-MATH-M413-28651 > Files > hw12-M413.pdf @ HTTP Spring 2022 Learn more about hw12-M413.pdf your Ca...00 series Account Home Download hw12-M413.pdf (98.8 KB) Announcements APR 25 Dashboard ZOOM Syllabus HS TRANSCRIPTS HW 12 Pages Courses Assignments (1) Prove that the function f(x) = 1 is not uniformly continuous on (0, 1]. (Hint: find two sequences {an}nɛN and {zn}n€N such that |an – Zn|< but |f(xn) – f(zn)| 2 1 for all n.) TXT Groups Grades 1 text (2) Prove that the function f(x) = Vr is uniformly continuous on [-1,0). (Hint: follow the example of f(x) = V from class, but considering the sets [-1,1] and [1/2, 0) ) stv People Calendar (3) Prove that the piece-wise function defined by Student Engagement Roster (Student) 1 3x - - if x < -2 Inbox Course f(x) = Relocated Items 11 if x = -2 Quiz 12 2 Questionnaire x2 + 5x + if x > -2 History Circleln is integrable on (-4, 7]. (Hint: do not use upper and lower sums, use a theorem) w Circleln (Faculty) TXT P Help text 2 Quiz 11 Page 2 of 2 696 words English (United States) Focus + 160%
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