(1.) Let f and g be scalar functions with continuous first and second order partial derivatives on a region E that is surrounded by a closed, piecewise-smooth surface S. (a.) Prove that Пр fvg.ñ dS by dis Thui = [[[ ( ƒV³g + ▼ ƒ · ▼g)dV E ffffg.nds SSS 7. (fig) dv E SSS [f\s+f. Gg] dv E - SSS [D'S + FF. Fg ] dv E 10 (b.) Use your result from (a.) to prove: ff(t▼g – g▼ƒ) · í · n dS= S [[[ ( ƒ V² 9 — gv² f ) V E v j] SSS [FD ² 9 + 5 OF ] dv - SSSB P² +ƒ¥3] dv E = E f+ dv. $$] [ou's + 1580-070 - 0/03/20 SSS (SS [f=g-gr²f] dri (555803-305]4+ . 10
(1.) Let f and g be scalar functions with continuous first and second order partial derivatives on a region E that is surrounded by a closed, piecewise-smooth surface S. (a.) Prove that Пр fvg.ñ dS by dis Thui = [[[ ( ƒV³g + ▼ ƒ · ▼g)dV E ffffg.nds SSS 7. (fig) dv E SSS [f\s+f. Gg] dv E - SSS [D'S + FF. Fg ] dv E 10 (b.) Use your result from (a.) to prove: ff(t▼g – g▼ƒ) · í · n dS= S [[[ ( ƒ V² 9 — gv² f ) V E v j] SSS [FD ² 9 + 5 OF ] dv - SSSB P² +ƒ¥3] dv E = E f+ dv. $$] [ou's + 1580-070 - 0/03/20 SSS (SS [f=g-gr²f] dri (555803-305]4+ . 10
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please review and solve the following problem. The screenshot listed already has some work done and the correct answer listed. Please solve the problem and include an explanation of how the work was solved. Also, Please make sure to double check the answer provided matches up with the screenshot and the work is properly formatted so I am able to follow along. Thanks :)
![(1.) Let f and g be scalar functions with continuous first and second order partial derivatives on a region
E that is surrounded by a closed, piecewise-smooth surface S.
(a.) Prove that
Пр
fvg.ñ dS
by
dis Thui
=
[[[ ( ƒV³g + ▼ ƒ · ▼g)dV
E
ffffg.nds
SSS 7. (fig) dv
E
SSS [f\s+f. Gg] dv
E
- SSS [D'S + FF. Fg ] dv
E
10
(b.) Use your result from (a.) to prove:
ff(t▼g – g▼ƒ) · í
· n dS=
S
[[[ ( ƒ V² 9 — gv² f ) V
E
v j]
SSS [FD ² 9 + 5 OF ] dv - SSSB P² +ƒ¥3] dv
E
=
E
f+
dv.
$$] [ou's + 1580-070 - 0/03/20
SSS
(SS [f=g-gr²f] dri
(555803-305]4+
. 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4effdf1a-67d0-42fb-b95c-7c4b54ad0624%2F782c327c-8a6c-493b-988d-3d30b425c295%2Ffud84f_processed.png&w=3840&q=75)
Transcribed Image Text:(1.) Let f and g be scalar functions with continuous first and second order partial derivatives on a region
E that is surrounded by a closed, piecewise-smooth surface S.
(a.) Prove that
Пр
fvg.ñ dS
by
dis Thui
=
[[[ ( ƒV³g + ▼ ƒ · ▼g)dV
E
ffffg.nds
SSS 7. (fig) dv
E
SSS [f\s+f. Gg] dv
E
- SSS [D'S + FF. Fg ] dv
E
10
(b.) Use your result from (a.) to prove:
ff(t▼g – g▼ƒ) · í
· n dS=
S
[[[ ( ƒ V² 9 — gv² f ) V
E
v j]
SSS [FD ² 9 + 5 OF ] dv - SSSB P² +ƒ¥3] dv
E
=
E
f+
dv.
$$] [ou's + 1580-070 - 0/03/20
SSS
(SS [f=g-gr²f] dri
(555803-305]4+
. 10
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