Use the comparison test to show that lim ootu 6n +n³ 5n - n³
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Theorem 2.4.7 (Comparison Test) Suppose {an} and {bn} are sequences
such that VnEN, an ≤ bn.
(a) If lim an = +∞o, then lim bn
818
n→∞
=
+∞o.
(b) If lim bn = ∞, then lim an = -0.
n→∞
n→∞
Proof. (a) Suppose lim an = +∞o. Let M > 0. Then, by Definition 2.4.1,
818
no
Nn > no ⇒ an> M. Since VnE N, an ≤ bn, it follows that
n> no ⇒ bn > M. Therefore, lim bn = +∞o.
n18
(b) Exercise 5.
Transcribed Image Text:Use the comparison test to show that lim
ootu
6n +n³
5n - n³
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