Question

Find an equation f(D)y = 0 where f(D) is a polynomial of degree 4 in D such that y = e^(−x)xcos(x) is a solution. What is the general solution to the constructed equation f(D)y = 0?

As before, it is better to leave f(D) in factored form. Using our fast formulas, verify that f(D)y = 0 for the given y and your f(D). Be sure to note the appropriate numbered formulas used.

Answer #1

Answer:-

write the polynomial equation f(x) in factored form with leading
coefficient -2, and zeros -1(double root), 1 (single root), and 3
(single root).
A) write f(x) in factored form
B) What is its degree?
C) what is its y-intercept
D) sketch the graph showing the zeros and y-intercept

Find the exact solution(s) to the equation:
17x2=1720−x17x2=1720-x
x=x=
The polynomial P(x)P(x) of degree 4 has
a root of multiplicity 2 at x = 4
a root of multiplicity 1 at x = 0 and at x = -3
It goes through the point (5, 12)
Find a formula for P(x)P(x).
Leave your answer in factored form.
P(x)=P(x)=

Use Newton-Raphson to find a solution to the polynomial equation
f(x) = y where y = 0 and
f(x) = x^3 + 8x^2 + 2x
- 40. Start with x(0) = 1 and continue until (6.2.2) is
satisfied with e= 0.0000005.

Let f(x, y) = sin x √y.
Find the Taylor polynomial of degree two of f(x, y) at (x, y) =
(0, 9).
Give an reasonable approximation of sin (0.1)√ 9.1 from the
Taylor polynomial of degree one of f(x, y) at (0, 9).

Find the degree-2 Taylor polynomial for the function f(x, y) =
exy at the point (4, 0).

Consider the differential equation: y'' = y' + y
a) derive the characteristic polynomial for the differential
equation
b) write the general form of the solution to the differential
equation
c) using the general solution, solve the initial value problem:
y(0) = 0, y'(0) = 1
d) Using only the information provided in the description of the
initial value problem, make an educated guess as to what the value
of y''(0) is and explain how you made your guess

Find an equation for f(x), the polynomial of smallest degree
with real coefficients such that f(x) bounces off of the x-axis at
5, breaks through the x-axis at −1, has complex roots of −5−3i and
−4+2i and passes through the point (0,89).

Find an equation for f(x), the polynomial of smallest degree
with real coefficients such that f(x) breaks through the x-axis at
−5, breaks through the x-axis at −4, has complex roots of 5−i and
−3−5i and passes through the point (0,68).

let f(x)=cos(x). Use the Taylor polynomial of degree 4
centered at a=0 to approximate f(pi/4)

Find the Maclaurin polynomial (c = 0) of degree n = 6 for f(x) =
cos(2x). Use a calculator to compare the polynomial evaluated at
π/8 and cos(2π/8)

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