Prove: If fand g are continuous at xo then 2f(x) xX,. +4g(x) is contin. at
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
Please prove my question like attached format, please please
otherwise i will mark incorrect.
please prove in two columns
statement |. Justification
![Format/example
Stat ement
jushifiation
> Given e>o 3 6,>0, &70 such that
» BY the definition
IfW) - f(x.)] < %4 wheneves x-4,| < 8,
of Continuity
|< <q wheneves -,] < Sz
> since fi, S2>0, we
Can take min S6,,2
2> Let 8: min { $i,8,}
3> PROPESH1 of mod ulus
and simple algeusa
3> for 1X- X,1 < 8 , we have
E/2 + 6/2 : €
> Hence (2f+48) is Continuons at X, 9 BY the defininion o0
Confinu ous.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11ef8d96-c3e7-4839-b3f7-96c5df0beac7%2Fe68a3b07-d226-4c54-862e-705ef988759e%2Faxvgz1t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Format/example
Stat ement
jushifiation
> Given e>o 3 6,>0, &70 such that
» BY the definition
IfW) - f(x.)] < %4 wheneves x-4,| < 8,
of Continuity
|< <q wheneves -,] < Sz
> since fi, S2>0, we
Can take min S6,,2
2> Let 8: min { $i,8,}
3> PROPESH1 of mod ulus
and simple algeusa
3> for 1X- X,1 < 8 , we have
E/2 + 6/2 : €
> Hence (2f+48) is Continuons at X, 9 BY the defininion o0
Confinu ous.
Transcribed Image Text:Prove:
continuous at x.
are
If f and a
then 2flx)+4g(x)is
(x) is contin. at Xo.
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