The equilibrium points of the system dx/dt = (2 + x)(y - x) , dy/dt = (4 - x)(y + x) are
a) (0, 0), (-2, 2), (4, 4)
b) (0, 0), (2, -2), (-4, 4)
c) (0, 0), (2, -2), (4, -4)
d) (0, 0), (2, -2), (-4, -4)
The suitable Liapunov function for the system dx/dt = -x^3 + xy^2 , dy/dt = -2x^2 y - y^3 is
a) V(x, y) = x^2 + y^2
b) V(x, y) = x^2 + 2y^2
c) V(x, y) = 2x^2 + y^2
d) V(x, y) = 1/2 x^2 + y^2
The Fourier Cosine series of the function f(x) = 3 - x, 0 < x < 3 is
a) f(x) = 3/2 + 6/pi sum_{n=1}^{infinity} [(1 - cos(n pi))/n^2] cos(n pi/3 x)
b) f(x) = sum_{n=1}^{infinity} [(1 - cos(n pi))/n^2] cos(n pi/3 x)
c) f(x) = 3/2 + sum_{n=1}^{infinity} [(1 - cos(n pi))/n^2] cos(n pi/3 x)
d) f(x) = 3/2 + 6/pi^2 sum_{n=1}^{infinity} [(1 - cos(n pi))/n^2] cos(n pi/3 x)
The solution to the equation z/(1 - z) = 1 - 5i is
a) z = 27 - 5i
b) z = 27/29 - 5/29 i
c) z = 5 - 27i
d) z = 0 + 5i