(1) Determine whether each of the statements is true or false by fill/bubble in the appropriate choice. You do not have to show your work. (a) True False Suppose C₁ and C2 are two smooth curves joints point (x1,y1, 1) to the point (x2, y2, 22). Suppose for the vector field ♬ there exists a function ƒ such that ♬ = у. Then | F · dr'ds = . √ F. dr where f is our usual function with the appropriate required conditions may or may not Iff has continuous partial derivatives on R³ and C is be true. (b) True False any circle, then f. dr = 0. (c) True False : If F is path-independent, then Lo₂ F - dr = F. . dr where C1 and C2 are any path.
(1) Determine whether each of the statements is true or false by fill/bubble in the appropriate choice. You do not have to show your work. (a) True False Suppose C₁ and C2 are two smooth curves joints point (x1,y1, 1) to the point (x2, y2, 22). Suppose for the vector field ♬ there exists a function ƒ such that ♬ = у. Then | F · dr'ds = . √ F. dr where f is our usual function with the appropriate required conditions may or may not Iff has continuous partial derivatives on R³ and C is be true. (b) True False any circle, then f. dr = 0. (c) True False : If F is path-independent, then Lo₂ F - dr = F. . dr where C1 and C2 are any path.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please complete to the best of your ability
Transcribed Image Text:(1) Determine whether each of the statements is true or false by fill/bubble in the
appropriate choice. You do not have to show your work.
Transcribed Image Text:(a) True False Suppose C₁ and C2 are two smooth curves joints point
(x1,y1, 1) to the point (x2, y2, 22). Suppose for the vector field ♬ there exists
a function ƒ such that ♬ = у. Then | F · dr'ds =
.
√ F. dr where f is
our usual function with the appropriate required conditions may or may not
Iff has continuous partial derivatives on R³ and C is
be true.
(b) True
False
any circle, then
f. dr = 0.
(c) True
False
: If F is path-independent, then
Lo₂ F - dr =
F.
. dr
where C1 and C2 are any path.
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