ve the statement using the , & definition of a limit. 18 + 2x lim x → 1 5 = 4 en & > 0, we need 8 ---Select---✓ such that if 0 < |x-1| < 6, then 18+ 2x ose ---Select-- > |( ¹8 + ²x) - 4 | < 5 , then 0 < |x-1| < 6⇒ 18 + 2x 5 4 - 4 < E. Thus, lim x → 1 18+ 2x 5 = 4 by the definition of a limit. ---Select--- 18+ 2x 5 . But + |²x - ²1. - 1| < |x-1| <--Select--. So if we

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Prove the statement using the ɛ, & definition of a limit.
18 + 2x
lim
x → 1 5
Given & > 0, we need 8 ---Select---
--Select---
choose 6 =
---Select--- V
= 4
I
then 0
such that if 0 < |x-1| < 6, then
2x
|x-1| < 8⇒ |(18 + ²x) - 4|
5
18 + 2x
5
4
<&. Thus, lim
X→ 1
18 + 2x
5
= 4 by the definition of a limit.
---Select--- V
18 + 2x
5
But
- 4|
4 < E
2x - 2
|²x=²|
5
< ε #
2
|||x − 1| < ɛ ⇒ |x − 1| < |---Select--- --
5
So if we
Transcribed Image Text:Prove the statement using the ɛ, & definition of a limit. 18 + 2x lim x → 1 5 Given & > 0, we need 8 ---Select--- --Select--- choose 6 = ---Select--- V = 4 I then 0 such that if 0 < |x-1| < 6, then 2x |x-1| < 8⇒ |(18 + ²x) - 4| 5 18 + 2x 5 4 <&. Thus, lim X→ 1 18 + 2x 5 = 4 by the definition of a limit. ---Select--- V 18 + 2x 5 But - 4| 4 < E 2x - 2 |²x=²| 5 < ε # 2 |||x − 1| < ɛ ⇒ |x − 1| < |---Select--- -- 5 So if we
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