4. Consider the logistic map f(x) = (1+ v6)x(1 – x) • Find the fixed point of 2-periodic cycle. • Determine its stability.

Q: EXERCISE 1. Find equation 2. For the E different- Xフ5 -h (x 5oɔ 9-T)(XUIS h+ X) =(x) J () a) f(x) =…

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Q: If the moment-generating function of X is M(t)= e, then the moment-generating 3t function of Y=1+-X…

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Q: Let X ~ Poisson(λ). Derive the moment generating function of X and use that to find E(X3)

A: Solution: Let X~Poisson(λ) The probability distribution of X is  P(x)=e-λλxx!    x=0,1,2,3,..

Q: 5- The equation (y`-y =e2x ) is : ( linear, exact, separable, Bernoulli )

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Q: 13.3.9 Evaluate -x)-Pdx a beta function. as

A: Use the property of beta function to evaluate this integral.

Q: 1. Consider the model for population growth below. Use a phase line analysis to sketch solution…

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Q: For the discrete logistic equation xt + 1 = Cxt(1 – Xt) and the given values of xo and c, calculate…

A: Let's find.

Q: 3t If the moment-generating function of X is M(t) = e, then the moment-generating function of Y=1+-X…

A: The provided information is: The moment generating function of X is given blown:

Q: 3) Show that for any constants M, k, and a, the function (",) A(1 - ) y(t) 1 ·M|1+tanh ´k(t – a)…

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Q: 11

A: Condition:

Q: Theorem 17-1. If T, is a consistent estimator of y(0) and y {y(0)} is a continuous function of y(0),…

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Q: Test whether any of the functions given in options (i), (ii), and (or) (iii) is (are) the solution…

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Q: 10.2.2 Use a cobweb to show that x* =0 is globally stable for 0<r< Tin the 1 logistic map.

A: As per the question we have to construct the cobweb diagram for the logistics map : xn+1 = rxn(1-xn)…

Q: 43. If f is differentiable and is periodic with period T, show that f' is also periodic with period…

A: First we prove that f'(x) is periodic by definition of derivative. Then we give an example to prove…

Q: (a) Show whether if 0<x <1, f(x) = 2 - x if 1<x < 2 is a Dirichlet function.

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Q: |1) discuss the physical meanings of time and spatial derivatives of the following PDE, and 2)…

A: Given, a PDE ρcp∂T∂t+∇·k∇T=0 part 1 first we have to discuss the physical meaning of time and…

Q: 1.The general solution of a 2nd order non-homogenous linear ODE of the form y" + p(x)y/ + q(x)y =…

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Q: Consider the equilibrium O of the continuous-time system given by å = Ax,where A E R²×". Which of…

A: This is a problem of the Dynamical system, a system of the differential equations.

Q: 2. Consider the continuous time model = rz - 1+z with r being any real value. Determine the steady…

A: The given continuous time model is x'=rx-x1+x2. Let fx=rx-x1+x2. Therefore the given model can be…

Q: 0. Suppose that x is the yield to maturity with continuous compounding on a zero-coupon bond that…

A: dB =[ (?B/?x) a(x0-x) + ?B/?t + ( 1/2) (?2B/?x2) s2x2] dt + (?B/?x)sxdz Since: B= e -x(T-t) The…

Q: Example 23 : Form the partial differential equation by eliminating the arbitrary function z= f(x? +…

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Q: Consider a delayed logistic equation of the form z(t + At) = z(t) + ar(t) (1– z(t – 2At)' K (a)…

A: Given: Let us consider the given delayed logistic equation of the form, xt+∆t=xt+αxt1-xt-2∆tK and…

Q: 32. In Example 4 of Section 1.2, we examined how CO2 concentrations (in ppm) have varied from 1974…

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Q: Consider a logistic regression system with two features x1 and x2. Suppose 00 = 5, 01 = 0, 02= 0,…

A: In logistic regression, the hypothesis function hθx is a sigmoid function which returns the values…

Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…

A: For any non linear function, to find the existence of its solution between an interval there should…

Q: Exercise (4.5) Recall that d dx Use this result and the chain rule to

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Q: a minimal realization of H(s). For any feedback gain realization for the corresponding Hƒ(s).

A: Given, (A, B) be a minimal realization of H(s).To prove: (A-BK, B) is a minimal realization for the…

Q: Assume that the growth of peacocks obey the rule dP : p³ – 17P² – 38P dt - Here P represents the…

A: According to question given that dPdt=P3-17P2-38P

Q: The following problem involves an equation of the form dt f(y). Sketch the graph of f(y) versus y,…

A: In this question, we have given a differential equation dydt=y(y-4)(y-8) we need to find the…

Q: Consider the IVP dy = (). Iy(20 -- y), y(0) = 1. dt %3D (a) Solve the IVP, finding y explicitly as a…

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Q: b) Let = .5P – 50. Find the equilibrium solution for P. Furthermore, determine whether P is dt…

A: To find the equilibrium solution for P

Q: 1.)Integrate: ∫(x+1)(x+2)^6dx Group of answer choices a.)(2/56) (7x + 6)(x + 2)7 + C b.)(2/56)…

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Q: 2 Discuss the stability of equilibrium points of the following ODE: { (2 = -r³ + y°, y = -x.

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Q: Find a linear differential operator (of lowest order) that annihilates the given function: f (x) =…

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Q: The following problem involves an equation of the form = f(y). dy dt Sketch the graph of f(y) versus…

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Q: ² a -2

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Q: The following problem involves an equation of the form = f(y). dy dt Sketch the graph of f(y) versus…

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Q: 1) Find the equilibra and sketch the phase line of the autonomous ODE u' = u*(2 – u). Determine the…

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Q: Example 8.19. Use Romberg's method to compute dx 1 + x² correct to 4 decimal places.

A: Let y = 11+x2  and let I = ∫01dx1+x2take h = 0.5 =12The tabulated values of y are   x0 x1 x2 x…

Q: 1. Consider the model for population growth below. Use a phase line analysis to sketch solution…

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Q: Consider the autonomous differential equation (y + 1)²(²-4). dt Determine all the equilibria and…

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Q: In Exercises 25 , show that the given function satisfies the given partial differential equation. O…

A: The given function is  z = xey. . . ... (1) To prove that x∂z∂x = ∂z∂y

Q: (3-c) Use Laplace transform to solve the given differential equation with the same initial…

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Q: 1.The general solution of a 2nd order non-homogenous linear ODE of the form y" + p(x)y' + q(x)y =…

A: We have to check out

Q: the relationship between aphids, A, ( prey) and ladybugs, L, (preditor) can be described as follows:…

A: the critical point is find by comparing the derivative to zero.

Q: 13+ 7+1 The long-run behavior of r(t) is 1+-t

A: Long run behavior of given function can be calculated using leading terms of numerator and…

Q: 3) Show that for any constants M, k, and a, the function k(t – a) y(t) M1+tanh 2 y' satisfies the…

A: To Show- Show that for any constants M, k, and a, the function yt = 12M1 + tanhkt - a2 satisfies the…

Q: 5.2-9. Determine the constant c such that f(x) cx (1 – x)°, 0 < x < 1, is a pdf. |-

A: Given: fx=cx3×1-x6        0&lt;x&lt;1