Question

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

Answer #1

by mistake i have written 6
iterations, it is **5 iteration**.

**so after 5 iteration,**

**x= 1.91062806627**

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.

Compute three iterations of Newton Raphson method to find the
root of the following equations
i. f (x) = x3-x-1 with x0 = 2.5
ii. f (x) = sin(2x)-cos(x)-x²-1 with x0 = 2.0
iii. x exp(x) = 2 with x0 = 0.55

a)
Let y be the solution of the equation y ″ − y = 3 e^(2x)
satisfying the conditions y ( 0 ) = 2 and y ′ ( 0 ) = 3.
Find the value of the function f ( x ) = ln ( y ( x ) − e^x )
at x = 3.
b)
Let y be the solution of the equation y ″ − 2 y ′ + y = x −
2
satisfying the...

Find the root of the function given below that is greater than zero with the Newton-Raphson method. First guess value You can get x0 = 0
f (x) = x2 + x - 2

Let y be the solution of the equation
a)
y ′ = 2 x y, satisfying the condition y ( 0 ) = 1.
Find the value of the function f ( x ) = ln ( y ( x ) )
at the point x = 2.
b)
Let y be the solution of the equation
y ′ = sqrt(1 − y^2) satisfying the condition y ( 0 )
= 0.
Find the value of the function f ( x...

Show that f(x) = C1e4x +
C2e-2x is a solution to the differential
equation: y’’ – 2y’ – 8y = 0, for all constants C1 and
C2. Then find values for C1 and C2
such that y(0) = 1 and y’(0) = 0.

Let f(x,y)=2ex+y. Find the second-order Taylor polynomial for
f(x,y) at the point (0,0).
Group of answer choices
2+x+y+12x2+12y2
2x+2y+x2+y2
2+2x+2y+x2+2xy+y2
2−2x−2y+x2−xy+y2
None of the above.

use stoke's theorem to find ∬ (curl F) * dS where F (x,y,z) =
<y, 2x, x+y+z> and and S is the upper half of the sphere x^2
+ y^2 +z^2 =1, oriented outward

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).

The indicated function
y1(x)
is a solution of the given differential equation. Use reduction
of order or formula (5) in Section 4.2,
y2 = y1(x)
e−∫P(x) dx
y
2
1
(x)
dx (5)
as instructed, to find a second solution
y2(x).
y'' + 64y = 0; y1 =
cos(8x)
y2 =

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