Let f: (0, 1)→ R be bounded but such that lim f does not exist. Show that there are two sequences (x₂) and (v.) in (0, 1) with lim(x) = 0 - lim(y) but such that (f(x)) and (f(x)) x-0

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
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Let f: (0, 1)→ R be bounded but such that lim f does not exist. Show that there are two
x-0
sequences (x) and (y) in (0, 1) with lim(x) = 0 = lim(y), but such that (f(xn)) and (f(n))
exist but are not equal.
Transcribed Image Text:Let f: (0, 1)→ R be bounded but such that lim f does not exist. Show that there are two x-0 sequences (x) and (y) in (0, 1) with lim(x) = 0 = lim(y), but such that (f(xn)) and (f(n)) exist but are not equal.
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