If lim alx) =A and lim b(x) = B then lim alx)-b(x) = A-B メ→C Thm 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 Thm If lim alx) =A and lim b(x) = B then lim alx)• b(x) = A•B メ→C
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 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
Transcribed Image Text:If lim a(x) = A and lim b(x) - B
then
lim alx)-b(x) = A-B
メ→C
Thm
If lim alx) =A and lim b(x) = B
then
lim alx)•b(x) = A•B
メ→C
![Class work: If lim f(t) = F and lim
Espuilean
delta
fim (266) + 4 g(+)=2 F+46
then
Gruen: VE7O as >0 s.t 0<l+-cl<S;>1fle)-F/<
3.
35>0 s.t Oclt -cks=lg(t)-G|<E
Show: VE>O 3s̟ >0 s.t O<lt-cl<s(244)04 gle)-(2F+*r)) < E
Proof: O Given any
E> 0
need parentheses
Choose S= /min{Sins >O O Gruen eEN
%3D
whenever Oclt-cl< Sg
we have Oalt-c|<Si
Oby choice ofS;
In step
and defn of min
OGiven
O acband c=270
AND
O 154) -FI< AND Iglt)-GlaE/8
O 2lf(t\-FI<%½ AND 41glt)-6/<½
→ accbc
VI triangle inei
O12$(+)-2F+4glt)-46]< E
12f(t)+ 4g(t) - 2F - 46)<E
Final(24(t)+4glt)-(2F+46)| <E
also c=470
Qtrrangleineg
®+O algebna
QE D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5ecd8c8-e8a3-4cc1-8420-cec6453dde8c%2F69533d1e-dfa1-4326-89d9-da969676f337%2Fthrjnqi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Class work: If lim f(t) = F and lim
Espuilean
delta
fim (266) + 4 g(+)=2 F+46
then
Gruen: VE7O as >0 s.t 0<l+-cl<S;>1fle)-F/<
3.
35>0 s.t Oclt -cks=lg(t)-G|<E
Show: VE>O 3s̟ >0 s.t O<lt-cl<s(244)04 gle)-(2F+*r)) < E
Proof: O Given any
E> 0
need parentheses
Choose S= /min{Sins >O O Gruen eEN
%3D
whenever Oclt-cl< Sg
we have Oalt-c|<Si
Oby choice ofS;
In step
and defn of min
OGiven
O acband c=270
AND
O 154) -FI< AND Iglt)-GlaE/8
O 2lf(t\-FI<%½ AND 41glt)-6/<½
→ accbc
VI triangle inei
O12$(+)-2F+4glt)-46]< E
12f(t)+ 4g(t) - 2F - 46)<E
Final(24(t)+4glt)-(2F+46)| <E
also c=470
Qtrrangleineg
®+O algebna
QE D
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