Question

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.

Answer #1

Why Newton's Method works at x0=-2 in f(x) = x^3-2x+2?

Apply Newton's Method to f and initial guess
x0
to calculate
x1, x2, and x3.
(Round your answers to seven decimal places.)
f(x) = 1 − 2x sin(x), x0 = 7

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.

: Consider f(x) = 3 sin(x2) − x.
1. Use Newton’s Method and initial value x0 = −2 to approximate
a negative root of f(x) up to 4 decimal places.
2. Consider the region bounded by f(x) and the x-axis over the
the interval [r, 0] where r is the answer in the previous part.
Find the volume of the solid obtain by rotating the region about
the y-axis. Round to 4 decimal places.

Use Newton's method to approximate the solution to the equation
9ln(x)=−4x+6. Use x0=3 as your starting value to find the
approximation x2 rounded to the nearest thousandth.

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

2. Let f(x) = sin(2x) and x0 = 0.
(A) Calculate the Taylor approximation T3(x)
(B). Use the Taylor theorem to show that
|sin(2x) − T3(x)| ≤ (2/3)(x − x0)^(4).
(C). Write a Matlab program to compute the errors for x = 1/2^(k)
for k = 1, 2, 3, 4, 5, 6, and verify that
|sin(2x) − T3(x)| = O(|x − x0|^(4)).

3.8/3.9
5. Use Newton's Method to approximate the zero(s) of the
function. Continue the iterations until two successive
approximations differ by less than 0.001. Then find the zero(s) to
three decimal places using a graphing utility and compare the
results.
f(x) = 3 − x + sin(x)
Newton's Method: x=
Graphing Utility: x=
6. Find the tangent line approximation T to the graph
of f at the given point. Then complete the table. (Round
your answer to four 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. (Round your answer to four decimal places.) 2x^3 − 3x^2 +
2 = 0, x1 = −1

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