Question

Higher order recurrence relations:

Find the general solution to each recurrence

(a) an −6an−1 + 11an−2 −6an−3 = 0 for n ≥ 3.

(b) an −5an−2 + 4an−4 = 0 for n ≥ 4.

*hint* To factor a polynomial of degree 3 or more look for a root r = a then use long division (dividing by the linear factor r −a) to ﬁnd the cofactor (which will now be of degree one less). Repeat until you have factored completely into linear factors

Answer #1

Give the general form of a solution to recurrence an
= 2an-1 + 3an-2 + 3n
r^2-2r-3=0
Assume a0
general form: an = c1an-1 +
c2an-2 + · · · + ckan-k
+ f(n) where c1, c2, . . . , ck are real numbers and f(n) is some
function of n.

1. Find the general solution of the first order linear
differential equation: 2*x*dy/dx -y-3/sqrt(x)=0. sqrt() = square
root of ().
2. Are there any transient terms in the general solution?
Justify your answer.

Find the general solution of the given higher order differential
equation
y^(4) + 4y^(3) − 4y^(2) − 16y^(1) = 0
Derivatives of Y not power

1.)Find T5(x), the degree 5 Taylor polynomial of the function
f(x)=cos(x) at a=0.
T5(x)=
Find all values of x for which this approximation is within
0.003452 of the right answer. Assume for simplicity that we limit
ourselves to |x|≤1.
|x|≤
2.) (1 point) Use substitution to find the Taylor series of
(e^(−5x)) at the point a=0. Your answers should not include the
variable x. Finally, determine the general term an in
(e^(−5x))=∑n=0∞ (an(x^n))
e^(−5x)= + x + x^2
+ x^3 + ... = ∑∞n=0...

What tools could AA leaders have used to increase their
awareness of internal and external issues?
???ALASKA AIRLINES: NAVIGATING CHANGE
In the autumn of 2007, Alaska Airlines executives adjourned at
the end of a long and stressful day in the
midst of a multi-day strategic planning session. Most headed
outside to relax, unwind and enjoy a bonfire
on the shore of Semiahmoo Spit, outside the meeting venue in
Blaine, a seaport town in northwest
Washington state.
Meanwhile, several members of...

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