Hw3] If lim $(x)=c #0 then lim X>c f(x)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please solve homework question in the following format like in two columns: 

 

•statment          |             •justifications 

 

Note: My previous homework was cancelled due to not following format.

[I have attached the classwork for guidance]

i want to give you thumbs up. So please follow attached format

 

my humble request to follow format [ •statement     | •justifications]

Hw3] If lim f(×)=c +0 then lim
X>c f(x)
Transcribed Image Text:Hw3] If lim f(×)=c +0 then lim X>c f(x)
Please solve like this below class work sample
Classwork Prove the Sundwich Theorem
If lim f(x)=L = lim h(x) and fla)s g(x)sh (x)
%3D
メ→C
lim ga) =L
Then
>0
3.
Proof:OGiven
any
Choose S}= [min ES
Show: VE>O 3S20 s.l o <lx-cl<S°
Oby grven
E>O
こ
,choice
O whenever O<lx-cl<S9 @ZT
"defa
have
we
AND OclX-cl<sh
3.
OIf(^) -Ll<E AND Ih(a)-L|<E O Given
limflx) =L
O L-E<f(x)<Z+E AND L-{<h(x)<2+€
31-ム
→と
wil フイメ
O la-blac t>
O L-E< {6)= g(«) s h (^)<L+ E Gstep4 and given
5 Step4 and given
3 +7>
O by step 5
O L-E<g(x) < L+E
Sina Ig(x)-L)<E
(final la-blacE
3-9ァクァ)-g
QED
Transcribed Image Text:Please solve like this below class work sample Classwork Prove the Sundwich Theorem If lim f(x)=L = lim h(x) and fla)s g(x)sh (x) %3D メ→C lim ga) =L Then >0 3. Proof:OGiven any Choose S}= [min ES Show: VE>O 3S20 s.l o <lx-cl<S° Oby grven E>O こ ,choice O whenever O<lx-cl<S9 @ZT "defa have we AND OclX-cl<sh 3. OIf(^) -Ll<E AND Ih(a)-L|<E O Given limflx) =L O L-E<f(x)<Z+E AND L-{<h(x)<2+€ 31-ム →と wil フイメ O la-blac t> O L-E< {6)= g(«) s h (^)<L+ E Gstep4 and given 5 Step4 and given 3 +7> O by step 5 O L-E<g(x) < L+E Sina Ig(x)-L)<E (final la-blacE 3-9ァクァ)-g QED
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