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If lim alx) = A and lim b(x)= B then lim alx)-b(x) = A-B メ→C

If lim alx) = A and lim b(x)= B then lim alx)-b(x) = A-B メ→C

Advanced Engineering Mathematics
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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Please solve homework (hw2) question in the THEOREM FORMAT like in two columns: 

•statment          |             •justifications 

 


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

[I have attached the classwork for format guidance]

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

Hw2It lima(x) = A and lim b(x)= B lim alx)-b(x) - A - B then メ→C Thm If lim alx) =A and lim b(x)= B then lim alx)•b(x) = A•B メ→C
Transcribed Image Text:Hw2It lima(x) = A and lim b(x)= B lim alx)-b(x) - A - B then メ→C Thm If lim alx) =A and lim b(x)= B then lim alx)•b(x) = A•B メ→C
Class work format 4 4 Classwork Prove the Sundwich Theorem If lim f(x)=L = lim h(x) and f(x)sg(x)sh (x] %3D Then lim grx) = L 37)7-(*)5) E's->0 35 O< SE o<3A : vanig Show: VE>O 3s20 s.l o <lx-c\<&° = Ig(^)-L)< E Proof:0Given any E> 0 Oby given Choose S}= [min ES > min { S フ O w henever Oclx-cl<S,3 @n choice ofmkn have AND Oclx-cl<sh limflx)=L O L-E<f(x)<Z+Ɛ AND L-E<h(al2+¢ *→C lim alx)=h →と O la-biac to O L-E< fla)< gl(x) <h (a)<L+ E ☺ stsp4 and given O L-E<g(x) < L+ E Sina) Ig(x)-L)< E )+97クフ)-9 Step4 O by step 5 inal) la-blecE b-CcacbrC QED
Transcribed Image Text:Class work format 4 4 Classwork Prove the Sundwich Theorem If lim f(x)=L = lim h(x) and f(x)sg(x)sh (x] %3D Then lim grx) = L 37)7-(*)5) E's->0 35 O< SE o<3A : vanig Show: VE>O 3s20 s.l o <lx-c\<&° = Ig(^)-L)< E Proof:0Given any E> 0 Oby given Choose S}= [min ES > min { S フ O w henever Oclx-cl<S,3 @n choice ofmkn have AND Oclx-cl<sh limflx)=L O L-E<f(x)<Z+Ɛ AND L-E<h(al2+¢ *→C lim alx)=h →と O la-biac to O L-E< fla)< gl(x) <h (a)<L+ E ☺ stsp4 and given O L-E<g(x) < L+ E Sina) Ig(x)-L)< E )+97クフ)-9 Step4 O by step 5 inal) la-blecE b-CcacbrC QED
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