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re true (there might be more than one true statement). converges to x ER then liminf(x)

re true (there might be more than one true statement). converges to x ER then liminf(x)

Advanced Engineering Mathematics
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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Mark all statements that are true (there might be more than one true statement). If a real sequence {x} converges to x E R then liminf(x) <x<limsup(x) . Let {x} If x is a cluster point of {x}, then liminf(x) <x<limsup(x). n Let {x} be a sequence of real numbers. Then limsup(x)=∞ if and only if {x} is not bounded above. Let {x} be a sequence of real numbers. If M ≤x, for all n € N, then M ≤ liminf(x). n be a sequence of real numbers. Then liminf(x)=-∞ if and only if {x} is not bounded above. n
Transcribed Image Text:Mark all statements that are true (there might be more than one true statement). If a real sequence {x} converges to x E R then liminf(x) <x<limsup(x) . Let {x} If x is a cluster point of {x}, then liminf(x) <x<limsup(x). n Let {x} be a sequence of real numbers. Then limsup(x)=∞ if and only if {x} is not bounded above. Let {x} be a sequence of real numbers. If M ≤x, for all n € N, then M ≤ liminf(x). n be a sequence of real numbers. Then liminf(x)=-∞ if and only if {x} is not bounded above. n
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