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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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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