Prove using the following definition of the limit of a sequencelim a, =g+ AVA la, - g|0 6 n>6What we read asA number g is a limit of an infinite sequence (a_n) if and only if for every postive number ɛ almost allexpressions of this sequence (a_n) are at a distance less than ɛ from the number g.Warming! Not use Hospital Rule or other until, direct by following definition.9n – 5|a) lim31812n? + 3n – 51.b) lim|8n? +14n oa

Answered: Ising lim a, =g AVA la, – gl0 6 n>6…

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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Question

Prove using the following definition of the limit of a sequence
lim a, =g+ AVA la, - g|<e
e>0 6 n>6
What we read as
A number g is a limit of an infinite sequence (a_n) if and only if for every postive number ɛ almost all
expressions of this sequence (a_n) are at a distance less than ɛ from the number g.
Warming! Not use Hospital Rule or other until, direct by following definition.
9n – 5
|
a) lim
3
18
1
2n? + 3n – 5
1.
b) lim
|
8n? +1
4
n oa

Expert Solution

Step 1

In the given question, concept of definition of limit is applied.

Limits

In mathematics, limits are the points at which a function approaches the output for the given input values. Limits are used to define integrals, derivatives, and continuity, among other things, in calculus and mathematical analysis. It is employed in the analysis process and always refers to the function's behaviour at a specific time.