Let f : (0. 1) → R be bounded but such that lim f does not exist. Show that there are two 1-0 sequences (x,) and (y,) in (0, 1) with lim(x,) = 0 = lim(y,), but such that lim (f (x,)) and lim (f(y,)) exist but are not equal.
Let f : (0. 1) → R be bounded but such that lim f does not exist. Show that there are two 1-0 sequences (x,) and (y,) in (0, 1) with lim(x,) = 0 = lim(y,), but such that lim (f (x,)) and lim (f(y,)) exist but are not equal.
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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![15. Let f : (0. 1) →R be bounded but such that lim f does not exist. Show that there are two
sequences (x,) and (v,) in (0, 1) with lim(x,) = 0 = lim(y,), but such that lim (f (x,)) and
lim (f(y,)) exist but are not equal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F871e9154-a0ff-45dd-bc27-ca399142d422%2F42177b5d-86a6-4445-9b2d-173baacb9f07%2Fxdzf4jq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:15. Let f : (0. 1) →R be bounded but such that lim f does not exist. Show that there are two
sequences (x,) and (v,) in (0, 1) with lim(x,) = 0 = lim(y,), but such that lim (f (x,)) and
lim (f(y,)) exist but are not equal.
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