Question

Utilize Newton's Method to estimate the root of 3 sin x - x = 0 for x > 0 correct to the sixth decimal places. Show all work below.

(Hint: start with x_{1} = 2)

Answer #1

Utilize Newton's Method to estimate the root of 2.2x5
- 4.4x3 + 1.3x2 - 0.9x - 4.0 = 0 with the
interval [-2.-1] to the sixth decimal place. Show all work and
estimations.
(Hint: Begin with x1 = -1.5)

Use
Newton's method to approximate the root of the equation to four
decimal places. Start with x 0 =-1 , and show all work
f(x) = x ^ 5 + 10x + 3
Sketch a picture to illustrate one situation where Newton's
method would fail . Assume the function is non-constant
differentiable , and defined for all real numbers

Use Newton's method to derive root of f(x) = sin(x) +
1. What is the order of convergence?

Use Newton's method to find the absolute maximum value of the
function f(x) = 8x sin(x), 0 ≤ x ≤ π correct to
SIX decimal places.

Use Newton's method with the specified initial approximation
x1 to find x3, the third
approximation to the root of the given equation.
x3 + 5x − 2 =
0, x1 = 2
Step 1
If
f(x) =
x3 + 5x − 2,
then
f'(x) = _____ x^2 + _____
2- Use Newton's method to find all roots of the
equation correct to six decimal places. (Enter your answers as a
comma-separated list.)
x4 = 5 + x
.

Let
f(x)=sin(x)+x^3-2. Use the secant method to find a root of f(x)
using initial guesses x0=1 and x1=4. Continue until two consecutive
x values agree in the first 2 decimal places.

Use Newton's method to find the value of x so that
x*sin(2x)=3
x0 = 5
Submit your answer with four decimal places.

Use Newton's method to approximate a root of
f(x) = 10x2 + 34x -14 if the initial approximation is
xo = 1
x1 =
x2 =
x3 =
x4 =

Use Newton's method to find all the roots of the equation
correct to eight decimal places. Start by drawing a graph to find
initial approximations.
3 sin(x2) = 2x

Newton's method: For a function ?(?)=ln?+?2−3f(x)=lnx+x2−3
a. Find the root of function ?(?)f(x) starting with
?0=1.0x0=1.0.
b. Compute the ratio |??−?|/|??−1−?|2|xn−r|/|xn−1−r|2, for
iterations 2, 3, 4 given ?=1.592142937058094r=1.592142937058094.
Show that this ratio's value approaches
|?″(?)/2?′(?)||f″(x)/2f′(x)| (i.e., the iteration converges
quadratically). In error computation, keep as many digits as you
can.

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