Let F(r, y) = P(x,y)i+Q(x, y)j. where P(r,y) = and Q(x,y) = 1² + y² 포2 + y2 and F(0,0) = 0. Among the following statements, find all True statement(s). (a) 2 = for all (x, y) # (0,0). %3D (b) F. dr = F. dr where 21 of 24 C1 : r(t) = (cos(t), sin(t)), 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let
F(x, y) = P(x, y)i+Q(x,y)j.
where
-y
P(x, y) =
and Q(x,y) =
%3D
r² + y²
x² + y?
and F(0,0) = 0. Among the following statements, find all True statement(s).
(a) 응 %3D for all (x, y) # (0, 0).
(b)
F. dr =
F. dr
where
21이
C1 : r(t) = (cos(t), sin(t)), 0<t < a
C2 : r(t) = (cos(t), – sin(t)), 0<t<n.
of 24
(c) F is conservative.
Select one:
(a), (b),(c)
(a), (b)
(b), (с)
(a), (c)
none of the other answers.
Transcribed Image Text:Let F(x, y) = P(x, y)i+Q(x,y)j. where -y P(x, y) = and Q(x,y) = %3D r² + y² x² + y? and F(0,0) = 0. Among the following statements, find all True statement(s). (a) 응 %3D for all (x, y) # (0, 0). (b) F. dr = F. dr where 21이 C1 : r(t) = (cos(t), sin(t)), 0<t < a C2 : r(t) = (cos(t), – sin(t)), 0<t<n. of 24 (c) F is conservative. Select one: (a), (b),(c) (a), (b) (b), (с) (a), (c) none of the other answers.
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