Question

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.

Answer #1

Process will be stopped when the two decimal places are equal

: 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 the secant method to estimate the root of
f(x) = -56x + (612/11)*10-4 x2 -
(86/45)*10-7x3 + (3113861/55)
Start x-1= 500 and x0=900.
Perform iterations until the approximate relative error falls below
1% (Do not use any interfaces such as excel etc.)

Consider a function f(x) =
2x3 − 11.7x2 +
17.7x − 5.
Identify the root of the given function after the third
iteration using the secant method. Use initial guesses
x–1 = 3 and x0 = 4.
CAN YOU PLZ SHOW ALL THE WORK. THANK YOU

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

Find the root of f(x) = exp(x)sin(x) - xcos(x) by the
Newton’s method
starting with an initial value of xo = 1.0.
Solve by using Newton’method until satisfying the tolerance
limits of the followings;
i. tolerance = 0.01
ii. tolerance = 0.001
iii. tolerance= 0.0001
Comment on the results!

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.

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)).

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 x1 = 2)

1. Let ?(?)=8(sin(?))? find f′(2).
2. Let ?(?)=3?sin−1(?) find f′(x) and f'(0.6).

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

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