consider the linear non-homogeneous recurrence relation of order three x(n)+x(n-1)-4x(n-2)-4x(n-3)=16 find the eigenvalues of the recurrence...

consider the linear non-homogeneous recurrence relation of order three x(n)+x(n-1)-4x(n-2)-4x(n-3)=16

find the eigenvalues of the recurrence relation, the closed form solution, and based on the dominant Eigen value determine if x(n) has longterm exponential growth

Expert Solution

Colby Messinger answered 6 months ago

Consider the following non-homogeneous linear recurrence: an =−an-1 +6an-2+125(8+1)·(n+1)·2n a0 = 0 a1 = 0 (b)...

Consider the following non-homogeneous linear recurrence: an =−an-1 +6an-2+125(8+1)·(n+1)·2n a0 = 0 a1 = 0 (b) Find the solution an(h) to the associated homogeneous linear recurrence. n (c) Find a particular solution anp to the non-homogeneous linear recurrence. (d) Find the general solution to the non-homogeneous linear recurrence.

Solve the given non-homogeneous recurrence relations: an = an-1 + 6an-2 + f(n) a) an =...

Solve the given non-homogeneous recurrence relations: an = an-1 + 6an-2 + f(n) a) an = an-1 + 6an-2 - 2n+1 with a0 = -4, a1= 5 b) an = an-1 + 6an-2 + 5 x 3n with a0 = 2, a1 = 5 c) an = an-1 + 6an-2 - 36n with a0 = 10, a1= 40

1. For the function P(x) = 4x^2 - 16 / x^2 -5x find the a) List X...

1. For the function P(x) = 4x^2 - 16 / x^2 -5x find the a) List X Intercept(s) if any b) List Y Intercept(s) if any c) List Horizontal Asymptote(s) if any d) List Vertical Asymptote(s) if any e) Domain 2. precalculus

3.Consider the system x=4x-y, y=2x+y (a) Write the system in matrix form and find the eigenvalues and...

3.Consider the system x*=4x-y, y*=2x+y (a) Write the system in matrix form and find the eigenvalues and eigenvectors of the matrix A. (b) Classify the fixed point at the origin (c) Find the general solution of the system (d) Solve the system subject to the initial condition

Solve the following recurrence relations. a. x(n) = x(n − 1) + 3 for n >...

Solve the following recurrence relations. a. x(n) = x(n − 1) + 3 for n > 1, x(1) = 0 b. x(n) = 5x(n − 1) for n > 1, x(1) = 6 c. x(n) = x(n/5) + 1 for n > 1, x(1) = 1 (solve for n = 5k )

find the general solution to the second order linear non-homogeneous differential equation (y"/2)-y' +y = cos...

find the general solution to the second order linear non-homogeneous differential equation (y"/2)-y' +y = cos x

Consider the following recurrence relation defined only for n = 2^k for integers k such that...

Consider the following recurrence relation defined only for n = 2^k for integers k such that k ≥ 1: T(2) = 7, and for n ≥ 4, T(n) = n + T(n / 2). Three students were working together in a study group and came up with this answer for this recurrence: T(n) = n * log2 (n) − n − log2 (n) + 8. Determine if this solution is correct by trying to prove it is correct by induction.

use the given zero to find the remaining zeros of each polynomial function 23. f(x)=x^3-4x^2+4x-16; zero;...

use the given zero to find the remaining zeros of each polynomial function 23. f(x)=x^3-4x^2+4x-16; zero; 2i 27. x^4-9x^3+21x^2+21x-130; zero: 3-2i Find the complex zeroes of each polynomial function. Write f in factored form. 35. f(x)=x^4+5x^2+4 I tried using Descarte's rule for questions 23 and 27, but I don't what to do after that. Also, after you explain the steps I need to solve the question, could you help understand why these steps are necessary?

Integral x^5-x^4+4x^3-4x^2+8x-4 / ( x^3+2)^3(x^2-1) dx

1) Find the Taylor series (to second order terms) of the function f(x,y) = x^2 −4x...

1) Find the Taylor series (to second order terms) of the function f(x,y) = x^2 −4x + y + 9 around the point x = 3, y = −1. 2)Explain why the corresponding Taylor Series (to third order terms) will be the same as the second-order series.

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