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Mark all true statements (there might be more than one true statement)

Mark all true statements (there might be more than one true statement)

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 true statements (there might be more than one true statement). O Let {*} be a sequence of real numbers and S = {x: k≥ n+1} for n = N. If a = inf(S) and = sup(S), for n N then liminf(x) = lim b n n n n→ ∞ If f {xn} i is a sequence of real numbers then liminf (x) <limsup(x „). x →x, x ER as n→ ∞o iff liminf(x) = limsup(x)=xE R. If Sx is a bounded sequence then both liminf(x and limsup(x, are cluster points. Let {x} be a sequence of real numbers and S = {x: k≥n+ 1} } for n = N. If a = inf(S) and b k = n , for n EN then limsup(x) sup($). ) = lim a n→ ∞
Transcribed Image Text:Mark all true statements (there might be more than one true statement). O Let {*} be a sequence of real numbers and S = {x: k≥ n+1} for n = N. If a = inf(S) and = sup(S), for n N then liminf(x) = lim b n n n n→ ∞ If f {xn} i is a sequence of real numbers then liminf (x) <limsup(x „). x →x, x ER as n→ ∞o iff liminf(x) = limsup(x)=xE R. If Sx is a bounded sequence then both liminf(x and limsup(x, are cluster points. Let {x} be a sequence of real numbers and S = {x: k≥n+ 1} } for n = N. If a = inf(S) and b k = n , for n EN then limsup(x) sup($). ) = lim a n→ ∞
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