Prove the hw7 that is "prove there is min" please follow the same above format which used in classwork
Prove the hw7 that is "prove there is min" please follow the same above format which used in classwork
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
Prove the hw7 that is "prove there is min"
please follow the same above format which used in classwork
![HW7:
Thm: If f: [a, b]→ R is continuous on
then 3 maximum M=max{f(x) | x e [a, b]}
[a, b]
3x, e [a,b] s.t f(x,)=M
Proof: O ¿f(x)|x ¢ [a,b]}
O by
has an uper
bound.
bounded
thm
O sup { s6o)lx¢[a,67} =5 exists ©
O Vje IN S-f<S is not @defn
classwork
bound of sup
an
"pper
O 3y; e {f)xE [a, b] } @ defn
S-fayjks
y=$(x;7 x;
"ppar
bóund
e [a,b] G defn
of our
set
OB-0
Thm
のf(x;,)→ fC)6 。
&lim f(x;)=lim
Timits
O by steps
step
+sandwich
Thm
4
lim y =S
kう。](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F596deb66-dd23-40c5-ac67-31db0d189646%2F22aa5590-8f54-4feb-bdf4-c571ec7e5b47%2Fhv05s4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:HW7:
Thm: If f: [a, b]→ R is continuous on
then 3 maximum M=max{f(x) | x e [a, b]}
[a, b]
3x, e [a,b] s.t f(x,)=M
Proof: O ¿f(x)|x ¢ [a,b]}
O by
has an uper
bound.
bounded
thm
O sup { s6o)lx¢[a,67} =5 exists ©
O Vje IN S-f<S is not @defn
classwork
bound of sup
an
"pper
O 3y; e {f)xE [a, b] } @ defn
S-fayjks
y=$(x;7 x;
"ppar
bóund
e [a,b] G defn
of our
set
OB-0
Thm
のf(x;,)→ fC)6 。
&lim f(x;)=lim
Timits
O by steps
step
+sandwich
Thm
4
lim y =S
kう。
![G lim $(x;)=lim Yn
O step4
+sandwich
Thm
limy =S
%3D
in the set
Oby steps 7-9
(リ f()= max
WIf a sup is
a set thenn
it
is the max.
f(x,)=maX QED.
HW7] Prove there
is a min,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F596deb66-dd23-40c5-ac67-31db0d189646%2F22aa5590-8f54-4feb-bdf4-c571ec7e5b47%2Fmg3l4es_processed.jpeg&w=3840&q=75)
Transcribed Image Text:G lim $(x;)=lim Yn
O step4
+sandwich
Thm
limy =S
%3D
in the set
Oby steps 7-9
(リ f()= max
WIf a sup is
a set thenn
it
is the max.
f(x,)=maX QED.
HW7] Prove there
is a min,
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