For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. 379. Minimize f ( x , y , z ) = x 2 + y 2 + z 2 when x + y + z = 9 and x + 2 y + 3 z = 20
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. 379. Minimize f ( x , y , z ) = x 2 + y 2 + z 2 when x + y + z = 9 and x + 2 y + 3 z = 20
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints.
379. Minimize
f
(
x
,
y
,
z
)
=
x
2
+
y
2
+
z
2
when
x
+
y
+
z
=
9
and
x
+
2
y
+
3
z
=
20
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.