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In: Advanced Math
Find the closed formula solution to each of the following recurrence relations with the given initial...
Find the closed formula solution to each of the following recurrence relations with the given initial conditions. Use an iterative approach and show your work! What is a_100? a) a_n=a_(n-1)+2,a_0=3 b) a_n=a_(n-1)+2n+3,a_0=4 c) a_n=2a_(n-1)-1,a_0=1 d) a_n=-a_(n-1),a_0=5
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Colby Messinger answered 1 year agoRelated Solutions
Find the closed formula solution to each of the following recurrence relations with the given initial...
Find the closed formula solution to each of the following
recurrence relations with the given initial conditions. Use an
iterative approach and show your work! What is
a100 ?
an=an-1+2,
a0=3
an=an-1+2n+3,
a0=4
an=2an-1-1,
a0=1
an=-an-1,
a0=5
Give exact solutions for each of the recurrence relations. Find the equilibrium values. Are the equilibrium...
Give exact solutions for each of the recurrence relations. Find
the equilibrium values. Are the equilibrium values stable?
a. x(n+1) = 1.5x(n) x(0) = 20
b. x(n+1) = -0.75x(n) + 5 x(0) = 10
c. x(n+1) = 1.2x(n) - 5 x(0) = 2
For each sequence given below, find a closed formula for an, the nth term of the sequence (assume...
For each sequence given below, find a closed formula
for an, the nth term of the sequence (assume the first
terms here are always a0) by relating it to another sequence
for which you already know the formula.
−1,0,7,26,63,124,…
an=(n^3)-1
−1,1,7,17,31,49,…
an=2n^2-1
0,10,30,60,100,150,.....
an=10*((n(n+1))/2)
2,3,6,14,40,152,…
an=
The first three are correct I can't figure out the
last one.
Solve the following recurrence relations: (find an asymptotic upper bound O(?) for each one) a. T(n)...
Solve the following recurrence relations: (find an asymptotic
upper bound O(?) for each one)
a. T(n) = T(2n/3)+T(n/3) + n^2
b. T(n) = √nT(√n) + n
c. T(n) = T(n-1)+T(n/2) + n
The base case is that constant size problems can be solved in
constant time (O(1)). You can use the induction, substitution or
recursion tree method
Find the general solution for the following ODEs. If initial condition is given, solve the initial...
Find the general solution for the following ODEs. If initial
condition is given, solve the initial value problem.
3) (D^4 − 13D^2 + 36I)y = 12e^x
4) (D^3 − D^2 − D + I)y = 0, y(0) = 0, Dy(0) = 1, D^2y(0) =
0
Find a closed formula for each of the following sequences. Show all work and explain your...
Find a closed formula for each of the following sequences. Show
all work and explain your answers.
(a) {1, 6, 17, 34, 57, 86, 121, . . .}, where
a0 = 1.
(b) an = 5an−1 + 4, a0
= 2
(c) an = 10an−1 −
21an−2, a0 = 6, a1 =
26.
In exercises 1–4, verify that the given formula is a solution to the initial value problem....
In exercises 1–4, verify that the given formula is a solution to
the initial value problem.
2. Powers of t.
b) y ′ = t^3 , y(0) = 5: y(t) = (1/5)t^(4) + 5
3. Sines and cosines.
a) x′ = −y, y′ = x, x(0) = 1, y(0) = 0: x(t) = cost, y(t) =
sint
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
Solve each of the following ODEs. If initial conditions are given, give the unique solution. d)...
Solve each of the following ODEs. If initial conditions are
given, give the unique solution.
d) y''' − 5y'' + 2y' + 8y = 0, y(0) = 2, y'(0) = −1, y''(0) =
−5
e) y''' + 9y'' + 27y' + 27y = 0, y(0) = 2, y'(0) = 0, y''(0) =
3
a) x^2y'' + xy' + 4y = 0, x > 0
b) x^2y'' − 6y = 0, x > 0, y(1) = y'(1) = 5
c) x^2y''...
1) Find the solution of the given initial value problem and describe the behavior of the...
1) Find the solution of the given initial value problem and
describe the behavior of the solution as t → +∞
y" + 4y' + 3y = 0, y(0) = 2, y'(0) = −1.
2) Find a differential equation whose general solution is
Y=c1e2t + c2e-3t
3) Determine the longest interval in which the given initial
value problem is certain to have a unique twice-differentiable
solution. Do not attempt to find the solution t(t − 4)y" + 3ty' +
4y...
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