13. Use phase plane analysis to analyze the solutions to the dynamical system b(n 1) -[2 - b(n)(n) 3 in the first quadrant. 13. Use phase plane analysis to analyze the solutions to the dynamical...
dy -X dx2 dt =2y-x dt 2. Consider the following system of equations: phase plane, showing only the first quadrant. (a) Graph the nullclines on a (b) Find the fixed points (there are two) to determine the nature of each fixed point (i.e., source, sink, saddle, and (c) Use Jacobian analysis whether it is a node or spiral). (d) Draw the flow arrows in each region of your phase plane from part (a). You may use a computer to help...
24. Consider the dynamical system A(n1) 3.6A(n) 3.6.A(n) (a) Find a 2-cycle for this system. (b) Show that this 2-cycle is unstable by showing that 24. Consider the dynamical system A(n1) 3.6A(n) 3.6.A(n) (a) Find a 2-cycle for this system. (b) Show that this 2-cycle is unstable by showing that
(curl F) n dS Use Stokes' Theorem to calculate 8) F-5yi - 6xj + 2z^k; C: the portion of the plane 6x + 7y + 4z -6 in the first quadrant A) B) 0 C) -11 D) 7 (curl F) n dS Use Stokes' Theorem to calculate 8) F-5yi - 6xj + 2z^k; C: the portion of the plane 6x + 7y + 4z -6 in the first quadrant A) B) 0 C) -11 D) 7
3. Continuous dynamical systems - Dimension 2 (a) Suppose the ODE system describes a continuous dynamical system in two dimensions (here f: R2 + R and g: R² R are two functions with smooth partial derivatives). Draw the corresponding vector field in the case that f(x,y) = x2 - y2 8(x, y) = x+y+1 and argue that (x,y) = R2 such that f(x,y) = g(x,y) = 0 are fixed points of the dynamical system above.
2) The region R in the first quadrant of the xy-plane is bounded by the curves y=−3x^2+21x+54, x=0 and y=0. A solid S is formed by rotating R about the y-axis: the (exact) volume of S is = 3) The region R in the first quadrant of the xy-plane is bounded by the curves y=−2sin(x), x=π, x=2π and y=0. A solid S is formed by rotating R about the y-axis: the volume of S is = 4) The region bounded...
Given A in Quadrant 1, with sin A=2/15, and B in Quadrant 1, With tangent B=13/15 find cosine A+B given A in Quadrant 1, with Sin=A 6/100, and B in quadrant 1, with tangent B=17/10 find tangent A+B PLEASE EXPLAIN IN DETAIL IF YOU CAN. i am really confused on how to even being to solve this
11. Match each linear system with one of the phase plane direction fields. 1 -3 a. 2 3 1 3 b. _ 2 1 1 0 C. 0 3 1 d 0 2 y B L L 11. Match each linear system with one of the phase plane direction fields. 1 -3 a. 2 3 1 3 b. _ 2 1 1 0 C. 0 3 1 d 0 2 y B L L
Consider the following system: dx/dt=y(x^2+y^2-1) dy/dt= -x(x^2 +y^2-1) Find the equilibrium solution. 13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of 13. Consider the following system dx dy (e) Find the equilibrium solutions (0 Use Maple to sketch a phase portrait (me to understand the qualitative behavior of
use the info. given below to find sin(a-b) cos a= 5/13, with a in quadrant IV cos b= -5/13, with b in quadrant III O TRIGONOMETRIC IDENTITIES AND EQUATIONS Sum and difference identities: Problem type 3 Use the information given below to find sin(a - b). COS 7 5 with a in quadrant IV 13 5 with B in quadrant III 13 cos B 1 Give the exact answer, not a decimal approximation. sin (a - b) = 0 8...
3 For the autonomous equation dN/dt NON - 2)(N - 5)2, (a) What are the equilibrium values of N, i.e., the solutions with N(t) constant? (b) Sketch families of solutions in the t-N plane (c) If a solution of the differential equation in this problem has the initial condition NO) 2.1, what happens to that solution after a long time? 3 For the autonomous equation dN/dt NON - 2)(N - 5)2, (a) What are the equilibrium values of N, i.e.,...