1. Solve these recurrence relations:
a. , Initial condition:
b.
c. , Initial conditions:
1. Solve these recurrence relations: a. , Initial condition: b. c. , Initial conditions: We were...
For these recurrence relations, solve for general equation using characteristics and particular. Use initial condition if given. a. fn+1 = 1 Initial condition: fo = 2 b. fn+1 -fn-n=0 n-1 1+fi = fn+1 Initial conditions: fo = 1, f1 = 1, n > 1 i=0
Which of the following is the solution to the differential equation with the initial condition y(1) = -1/2 A. B. C. D. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
By using Karush–Kuhn–Tucker (KKT) Conditions and condition for lamda solve the example: We were unable to transcribe this imageExample: Consider the constrained minimization problem: 2 4 3 min xi + X2 VER? 2 8 subject to 1- Xı – x2 > 0 1- xy + x, 20 1+ x - x2 > 0 1+x+x, 20.
Solve the harmonic oscillator motion for initial conditions x(0) = 0, V(0) = V0 in the case of (a) underdamped (b) overdamped We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
given from notes and The derivative relations are and d/dx [x^(-v) I_v(x)] = x^(-v) I_(v+1) Sorry, no image of that one in notes. The relations we after are following: From the derivative relations for I, (x) in the notes, derive the recurrence relations for I, (x) We were unable to transcribe this imageWe were unable to transcribe this imagedr 2v 山
8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0 (a) Find the generating function for an and then solve for an b) What is the homogeneous recurrence relation that an satisfies? (c) Repeat (a) and (b) for bn 72. 8. Consider the following simultaneous homogeneous recurrence relations: 3a-12bn-1 bn-an-1 + 2bn-1 for n > 1, with initial conditions ao 1 and bo - 0...
7. Find the solution of each of these recurrence relations with the given initial conditions. Use appropriate summation formulas to simplify your answers. a) an = (n + 1)an-1, ao = 5 The solution is: b) an=2an-1-3, a, = 5 c) an = An-1 + n-3, ao = 7
5. Find the closed form solutions of the following recurrence relations with given initial conditions. Use forward substitution or backward substitution as described in Example 10 in the text. (a) an = −an−1, a0 = 5 (b) an = an−1 + 3, a0 = 1 (c) an = an−1 − n, a0 = 4 (d) an = 2nan−1, a0 = 3 (e) an = −an−1 + n − 1, a0 = 7 5. Find the closed form solutions of the...
a) Show that b) For non zero integers exists in investigate the conditions on that are equivalent to the condition We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Find an appropriate recurrence relation with initial conditions, and solve the recurrence relation. Find a recurrence relation for the number of ways to arrange cars in a row with n spaces if we can use Cadillacs or Hummers or Fords. A Hummer requires two spaces, whereas a Cadillac or a Ford requires just one space.