Bölüm 3 1) Let f:(0, 00) -→ R conti nu ous and bonded be a L{f3 (s) = Je Se fltldt function. Let -st exist for an a € (0,o) and be defined e au flu) du as tt (0,00). (s-a)t $ (+) dt a) Prove that integra l is inter val [b, o) for all the e unifor mly convergent in the b> a. -) Prove the equality 8. - St e (s-a) -(s-a)t O (4) dt e

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Bölüm 3
conti nu ous and
bounded
be a
1) Let
f: (0, 00) -R
L{f3 (s) = Sest
f(t)dt
t.
exist for
function. Let
an a € (0,0) and
$(+)=eau flu)du
be defined
as
tt (0,00).
Sesie()dt integra l is
Je (s-ajt
Prove that
$ (+) dt integra l is
a)
the
unifor mly con vergent
inter val [b, o) for all
in
the
b> a.
b) Prove
the equality
- +P(+)J,?
f(t)dt = (s-a)
-st
e
O (+) dt , s>a
e
Transcribed Image Text:Bölüm 3 conti nu ous and bounded be a 1) Let f: (0, 00) -R L{f3 (s) = Sest f(t)dt t. exist for function. Let an a € (0,0) and $(+)=eau flu)du be defined as tt (0,00). Sesie()dt integra l is Je (s-ajt Prove that $ (+) dt integra l is a) the unifor mly con vergent inter val [b, o) for all in the b> a. b) Prove the equality - +P(+)J,? f(t)dt = (s-a) -st e O (+) dt , s>a e
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