In the following exercises, find the work done by force fiel d F on an object moving along the indicated path. 71. Force F ( x , y , z ) = z y i + x j + z 2 x k acts on a particle that travels from the origin to point (1, 2, 3). Calculate the work done if the particle travels:a. along the path (0,0,0) → .(1,0,0) → ’(1,2,0) → .(1,2,3) along straight-line segments joining each pair of endpoints: b. along the straight line joining the initial and final points. c. Is the work the same along the two paths? (1, 2, 3)
In the following exercises, find the work done by force fiel d F on an object moving along the indicated path. 71. Force F ( x , y , z ) = z y i + x j + z 2 x k acts on a particle that travels from the origin to point (1, 2, 3). Calculate the work done if the particle travels:a. along the path (0,0,0) → .(1,0,0) → ’(1,2,0) → .(1,2,3) along straight-line segments joining each pair of endpoints: b. along the straight line joining the initial and final points. c. Is the work the same along the two paths? (1, 2, 3)
In the following exercises, find the work done by force fiel d F on an object moving along the indicated path.
71. Force
F
(
x
,
y
,
z
)
=
z
y
i
+
x
j
+
z
2
x
k
acts on a particle that travels from the origin to point (1, 2, 3). Calculate the work done if the particle travels:a. along the path (0,0,0)
→
.(1,0,0)
→
’(1,2,0)
→
.(1,2,3) along straight-line segments joining each pair of endpoints:
b. along the straight line joining the initial and final points.
c. Is the work the same along the two paths? (1, 2, 3)
Q2) A: Find the region where ODEs has no limit cycle:
x = y + x³
y=x+y+y³
6
Q3)A: Given H(x,y)=x2-x+ y²as a first integral of an ODEs, find this ODES
corresponding to H(x,y) and show the phase portrait by using Hartman
theorem and by drawing graph of H(x,y)-e. Discuss the stability of
critical points of the corresponding ODEs.
Q/ Write Example
is First integral but not
Conservation system.
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
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