Let DEIR, xn be a sequence in [DEIR+correction Proof: Suppose D is closed. To prove xn ED 6-t xnxx Let xED = XEDC Since D is closed = Dc open. → =TE 76 s.t (x-E₂x+E) CDC- equation 1 Since xnx for given t>OTNE INS.t - 1xn-21²E +n²N = XVE (X-E₁ x + E) NEIN using equation 1 xn EDC #HEIN = E =XED. Conversely, Let xnxs.t. xtd. Let D is not closed = De → not open Thus, we have TXE DC sit. (1-E₂x +E) DC for X E70 any = (x-Ex+E) has atleast one pt in (DC)C= D. Choosing E=Yn For each nEIN, We enumerate such x as x₁, X₂, st x n = ( x ² + ₂ x + h) 00 nj = xn is a sequence in D v.t. xnx but =Du closed XEDC = E
Let DEIR, xn be a sequence in [DEIR+correction Proof: Suppose D is closed. To prove xn ED 6-t xnxx Let xED = XEDC Since D is closed = Dc open. → =TE 76 s.t (x-E₂x+E) CDC- equation 1 Since xnx for given t>OTNE INS.t - 1xn-21²E +n²N = XVE (X-E₁ x + E) NEIN using equation 1 xn EDC #HEIN = E =XED. Conversely, Let xnxs.t. xtd. Let D is not closed = De → not open Thus, we have TXE DC sit. (1-E₂x +E) DC for X E70 any = (x-Ex+E) has atleast one pt in (DC)C= D. Choosing E=Yn For each nEIN, We enumerate such x as x₁, X₂, st x n = ( x ² + ₂ x + h) 00 nj = xn is a sequence in D v.t. xnx but =Du closed XEDC = E
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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is this correct or no? if not please correct it
![Let DEIR, xn be a sequence in [DEIR] correction
Proof: Suppose D is closed.
To prove xn ED s-t xnxx
Let xED
= XEDC
since D is closed = Dc → open.
=TE 70 st
(x-E₂x+E) CDC- equation 1
Since xnx. for given E>OTNE INS.t
- 1xn- 21²E +n²N
= xnE (x-E₁ x + E) +MEIN
using equation 1 xn EDC #HEIN
= E
=XED.
Conversely, Let xnx s.t. xtd.
Let D is not closed
De not open
Thus, we have TxE DC sit.
(1-E₂x +E) & DC for
any
E70
= (x-E₂x + E) has at least one pt in (DC)C= D.
Choosing F = Yn
For each nEIN, we enumerate such x as X₁, X2,....
st x n = ( x - √ ₂ x + h). 00
J
= xn is a sequence in D s.t. xnx but
= Du closed
XEDC = E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faec36bf2-f3f0-4133-a0b2-246dadf54ad6%2F7313608a-451f-460a-b6ee-18529966c51a%2Fbxri1uo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let DEIR, xn be a sequence in [DEIR] correction
Proof: Suppose D is closed.
To prove xn ED s-t xnxx
Let xED
= XEDC
since D is closed = Dc → open.
=TE 70 st
(x-E₂x+E) CDC- equation 1
Since xnx. for given E>OTNE INS.t
- 1xn- 21²E +n²N
= xnE (x-E₁ x + E) +MEIN
using equation 1 xn EDC #HEIN
= E
=XED.
Conversely, Let xnx s.t. xtd.
Let D is not closed
De not open
Thus, we have TxE DC sit.
(1-E₂x +E) & DC for
any
E70
= (x-E₂x + E) has at least one pt in (DC)C= D.
Choosing F = Yn
For each nEIN, we enumerate such x as X₁, X2,....
st x n = ( x - √ ₂ x + h). 00
J
= xn is a sequence in D s.t. xnx but
= Du closed
XEDC = E
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