Let S = Qn(0, 1) and if m, n are coprime positive integers, define f(m/n)= 1/(m + n) (a) Prove that lim f (x) = 0 X-0^S (b) Prove that lim f (x) = 0 X→1^S (c) Prove that for any q E S, we have lim f (x) does not exist. x→q^S
Let S = Qn(0, 1) and if m, n are coprime positive integers, define f(m/n)= 1/(m + n) (a) Prove that lim f (x) = 0 X-0^S (b) Prove that lim f (x) = 0 X→1^S (c) Prove that for any q E S, we have lim f (x) does not exist. x→q^S
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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![Let S = Qn(0, 1) and if m, n are coprime positive integers, define f(m/n)= 1/(m + n)
(a) Prove that lim f (x) = 0
X→0^S
(b) Prove that lim f (x) = 0
X→1^S
(c) Prove that for any q E S, we have lim f (x) does not exist.
x→q^S](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7373726-0d35-46ca-aa27-97bcf9126f3a%2F902e6c44-1370-4f0d-8aaf-fae23375b4c7%2Fafvqj8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let S = Qn(0, 1) and if m, n are coprime positive integers, define f(m/n)= 1/(m + n)
(a) Prove that lim f (x) = 0
X→0^S
(b) Prove that lim f (x) = 0
X→1^S
(c) Prove that for any q E S, we have lim f (x) does not exist.
x→q^S
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