If (un)neN and (Un)neN are sequences that are bounded below, then the sequence (un Un)neN is bounded below. Select one: a. True, here is an example: (un)nÊN = (1, 1/2, 1/3, 1/4, ...) and (Un)neN = (0, 1/2, 3/4, 4/5, ...). O b. False, here is a counter-example: (Un)nÊN = (1, 2, 3, 4, ….) and (Un)neN = (−1, −1, −1, ···). c. True, it is bounded below by the product of a lower bound of (Un) nÊN and a lower bound of (Un)neN. O d. False, because the taking the product of un and Un increases the magnitude of their values and can make them larger and larger in the negative numbers.
If (un)neN and (Un)neN are sequences that are bounded below, then the sequence (un Un)neN is bounded below. Select one: a. True, here is an example: (un)nÊN = (1, 1/2, 1/3, 1/4, ...) and (Un)neN = (0, 1/2, 3/4, 4/5, ...). O b. False, here is a counter-example: (Un)nÊN = (1, 2, 3, 4, ….) and (Un)neN = (−1, −1, −1, ···). c. True, it is bounded below by the product of a lower bound of (Un) nÊN and a lower bound of (Un)neN. O d. False, because the taking the product of un and Un increases the magnitude of their values and can make them larger and larger in the negative numbers.
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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Transcribed Image Text:If (un)neN and (Un)neN are sequences that are bounded below, then the sequence
(un Un)neN is bounded below.
Select one:
a. True, here is an example: (Un)n=N
(Un)neN = (0, 1/2, 3/4, 4/5, ...).
=
(1, 1/2, 1/3, 1/4, …) and
b. False, here is a counter-example: (Un)nÊN = (1, 2, 3, 4, …) and
(Un)neN = (-1,-1,-1, ...).
c. True, it is bounded below by the product of a lower bound of (un)neN and a lower
bound of (Un)neN.
O d. False, because the taking the product of un and Un increases the magnitude of their
values and can make them larger and larger in the negative numbers.
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