H x,y E IR Ix+y I \x\ Ix + yl
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
100%
![Hw12 Fill in the missing justifications
Theorem: Vx,y e IR Ix+y Islxl+
ly!
Proof:
O xy slxyl = Ix]lyl ☺
and
2)
® 2×y s 21xl ly I
Ox*. 2xy • y°s x'+ 2 lxllyl* y² ®
3) x+
☺ x²+ 2 *y +y? </xl°+ 2 (x lyl+lyl*
© (x + y)² s (Ixl+lyl)²
<\xl*+ 2 [x\ ly]+lyl ☺
of
by Catb)= a*+ Zab+b?
with azx and b=y
and with a=lx| and bélyl
2
| x + y l?s(1xl+ly)?
< (1xl+lyl)
6.
(x + y/ s 1xI +lyl
QED](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffb6b3dc-3f5c-40ac-bd53-e6d430b351c6%2Fe2ae20da-451e-4404-bacd-7aad382391bd%2Fjppv8ao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Hw12 Fill in the missing justifications
Theorem: Vx,y e IR Ix+y Islxl+
ly!
Proof:
O xy slxyl = Ix]lyl ☺
and
2)
® 2×y s 21xl ly I
Ox*. 2xy • y°s x'+ 2 lxllyl* y² ®
3) x+
☺ x²+ 2 *y +y? </xl°+ 2 (x lyl+lyl*
© (x + y)² s (Ixl+lyl)²
<\xl*+ 2 [x\ ly]+lyl ☺
of
by Catb)= a*+ Zab+b?
with azx and b=y
and with a=lx| and bélyl
2
| x + y l?s(1xl+ly)?
< (1xl+lyl)
6.
(x + y/ s 1xI +lyl
QED
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