Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (2,0,0) to (2,0,4). a. The line segment x = 2, y = 0, 0≤z≤4 b. The helix r(t) = (2cos t)i + (2sin t)j + k, 0st≤2π c. The x-axis from (2,0,0) to (0,0,0) followed by the parabola Z=x² , y = 0 from (0,0,0) to (2,0,4) a. Find a scalar potential function f for F, such that F = Vf. OA. √ √x ²³ + xy + = = y³² + z = 2² + C 3) 1 ocx²+x²²+²+²+0 O E. The vector field F is not conservative. (2,0,4) Ish (0,0,0) -(2,0,0) x³ + xy + y² + z OD. x³ + xy + y² + ze² - e² + C O B. +ze² - e²+ C
Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (2,0,0) to (2,0,4). a. The line segment x = 2, y = 0, 0≤z≤4 b. The helix r(t) = (2cos t)i + (2sin t)j + k, 0st≤2π c. The x-axis from (2,0,0) to (0,0,0) followed by the parabola Z=x² , y = 0 from (0,0,0) to (2,0,4) a. Find a scalar potential function f for F, such that F = Vf. OA. √ √x ²³ + xy + = = y³² + z = 2² + C 3) 1 ocx²+x²²+²+²+0 O E. The vector field F is not conservative. (2,0,4) Ish (0,0,0) -(2,0,0) x³ + xy + y² + z OD. x³ + xy + y² + ze² - e² + C O B. +ze² - e²+ C
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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Transcribed Image Text:Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the
following paths from (2,0,0) to (2,0,4).
a. The line segment x = 2, y = 0, 0≤z≤4
b. The helix r(t) = (2cos t)i + (2sin t)j +
k, 0st≤2π
c. The x-axis from (2,0,0) to (0,0,0) followed by the parabola
Z=x²
, y = 0 from (0,0,0) to (2,0,4)
a. Find a scalar potential function f for F, such that F = Vf.
OA. √ √x ²³ + xy + = = y³² + z = 2² + C
3)
1
ocx²+x²²+²+²+0
O E. The vector field F is not conservative.
(2,0,4)
Ish
(0,0,0)
-(2,0,0)
x³ + xy +
y² + z
OD. x³ + xy + y² + ze² - e² + C
O B.
+ze² - e²+ C
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