my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.
my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.
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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2.20) my professor says I have to explain the steps in the solved problems in the picture. Not just copy eveything down from the text.
Transcribed Image Text:Least upper bound, greatest lower bound, limit superior, limit inferior
2.20.
Find the (a) L.u.b., (b) g.l.b., (c) lim sup ( lim ), and (d) lim inf (lim) for the sequence 2, -2, 1,-1, 1, –1, 1,
-1,....
(a) 1.u.b. = 2, since all terms are less than equal to 2, while at least one term (the 1st) is greater than 2 – e for
any e > 0.
(b) g.l.b. = -2, since all terms are greater than or equal to -2, while at least one term (the 2nd) is less than
-2 + e for any e > 0.
(c) lim sup or lim = 1, since infinitely many terms of the sequence are greater than 1 - e for any e > 0
(namely, all l's in the sequence), while only a finite number of terms are greater than 1 + e for any e >0
(namely, the 1st term).
(d) lim inf or lim =-1, since infinitely many terms of the sequence are less than –1 + e for any e > 0 (namely,
all –l's in the sequence), while only a finite number of terms are less than -1 - e for any e > 0 (namely,
the 2nd term).
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