Ans 1- Prove L{et coskt} = S+a We Know that ast Hen L{eat.coskt}= fat at coskt dt -st-at • coskt dt (Sta)t dt - (1) let --(S4)t e I= . cos kt dt -(2) Coskt by usng frmula integaadion f two functions - (sta)t Lim Coskt. e - Coso. e Sensmet) - (s+4}t dt -(s+a) -ksinict) -(S+a}t Um coskt e S+a sinkt. ēGta)t dt S+a if bm ft)=0 and g) We know that is beuided then -(sta)t Lim e Нете = im And coskt betndo d on IR. |coskt| | TS for all t elR
Ans 1- Prove L{et coskt} = S+a We Know that ast Hen L{eat.coskt}= fat at coskt dt -st-at • coskt dt (Sta)t dt - (1) let --(S4)t e I= . cos kt dt -(2) Coskt by usng frmula integaadion f two functions - (sta)t Lim Coskt. e - Coso. e Sensmet) - (s+4}t dt -(s+a) -ksinict) -(S+a}t Um coskt e S+a sinkt. ēGta)t dt S+a if bm ft)=0 and g) We know that is beuided then -(sta)t Lim e Нете = im And coskt betndo d on IR. |coskt| | TS for all t elR
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
(1) how did you come up with the solution? PLEASE EXPLAIN IN DETAIL because I'm going to make a script out of it
![Then
-(Sta)t
coskt. e
Lim
Then
I= -_
Sta
[o -1] -K Teeta)t
• Sinkt dt
Sta
- (S44) t0
•e
d Sinkt)
K
Sta
- (sta)
(St4)t
Sinkt. e
sino. e
Sta
Sta
K. coskt
-(sta)
FP
2.
-(Sta)teslet dt
-L+K_ (o-0) - K
(S+aj2
Sta
using (3)
Since, Sinkt is also
bounded on IR
|Sinktl <1 for all teIR
- I=
Sta
+o
(s+a)2.
K2
I =
6+4)2
S+9
=> I(1+
_k²
S+a
(S+a)2
S+a
(S+9)2
s+a)
From ) and (2), we get
S+a
Hence proved
(S+a)2 + K2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdde3ae2a-42ac-433e-9f60-e7d93b0f2f12%2F7487973f-7139-4b06-be5c-0df62788c03d%2F4zzci0d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Then
-(Sta)t
coskt. e
Lim
Then
I= -_
Sta
[o -1] -K Teeta)t
• Sinkt dt
Sta
- (S44) t0
•e
d Sinkt)
K
Sta
- (sta)
(St4)t
Sinkt. e
sino. e
Sta
Sta
K. coskt
-(sta)
FP
2.
-(Sta)teslet dt
-L+K_ (o-0) - K
(S+aj2
Sta
using (3)
Since, Sinkt is also
bounded on IR
|Sinktl <1 for all teIR
- I=
Sta
+o
(s+a)2.
K2
I =
6+4)2
S+9
=> I(1+
_k²
S+a
(S+a)2
S+a
(S+9)2
s+a)
From ) and (2), we get
S+a
Hence proved
(S+a)2 + K2
![1
Ans
Prove
L{Et coskt
S+a
We know that
L{ftt}= Sest f4) dt
Then
Leat.coskt} = ft ent.coskt dt
-st -at
e
• coskt dt
-- ()
Let
-(Sta)t
e
I=
cos kt dt
- (2)
as
-(S+ajt
Coskt
by using fermula indegadion f two functions
-(sta)t
- coso.
i Lim Coskt.e
(S+a) ltj
:(s+a}t
dt
-(Sta)
k sinict) e
-(Stajt
Ix]
Lim coskt e
Sta
sinkt. ēst)t dt
S+a
and g
Um ft)=0
if
too
We know that
is
bounded
then
Lim fCt).glt) = o -3)
-(sta)t
Lim e
= Lim t -
Here
on IR. Icoskt|<1
for all t eIR
And
coskt
beundo d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdde3ae2a-42ac-433e-9f60-e7d93b0f2f12%2F7487973f-7139-4b06-be5c-0df62788c03d%2Fssd6dgo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1
Ans
Prove
L{Et coskt
S+a
We know that
L{ftt}= Sest f4) dt
Then
Leat.coskt} = ft ent.coskt dt
-st -at
e
• coskt dt
-- ()
Let
-(Sta)t
e
I=
cos kt dt
- (2)
as
-(S+ajt
Coskt
by using fermula indegadion f two functions
-(sta)t
- coso.
i Lim Coskt.e
(S+a) ltj
:(s+a}t
dt
-(Sta)
k sinict) e
-(Stajt
Ix]
Lim coskt e
Sta
sinkt. ēst)t dt
S+a
and g
Um ft)=0
if
too
We know that
is
bounded
then
Lim fCt).glt) = o -3)
-(sta)t
Lim e
= Lim t -
Here
on IR. Icoskt|<1
for all t eIR
And
coskt
beundo d
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