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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
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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(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
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
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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