Choose the letter of the correct answer. Which of the following letters are true (you can choose more than 1) If (x_n) is a sequence in R that converges to LE R then which of the following is (are) not true? (a) for any E>0, for all natural number N we have Ix_n-L<ɛ whenever n2 N. (b) lim inf (x_n) = L = lim sup (x_n). (c) there is a real number M> 0 s.t. x.nl s M. (d) for any >0, there exists NEN s.t. lx_m-x_n
Choose the letter of the correct answer. Which of the following letters are true (you can choose more than 1) If (x_n) is a sequence in R that converges to LE R then which of the following is (are) not true? (a) for any E>0, for all natural number N we have Ix_n-L<ɛ whenever n2 N. (b) lim inf (x_n) = L = lim sup (x_n). (c) there is a real number M> 0 s.t. x.nl s M. (d) for any >0, there exists NEN s.t. lx_m-x_n
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:Choose the letter of the correct answer.
Which of the following letters are true (you can choose more than 1)
If (x_n) is a sequence in R that converges to LE R then which of the following is (are) not true?
(a) for any >0, for all natural number N we have Ix_n-L<ɛ whenever n2 N.
(b) lim inf (x_n) = L = lim sup (x_n).
(c) there is a real number M> 0 s.t. lx_n/ s M.
(d) for any >0, there exists NEN s.t. lx_m-x_nl<e for some mn2N.
(e) (x_n) is bounded and monotonic.
(0) every subsequence of (x_n) converges to L
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