Question

solve cos(x)=x^2 using Newton's Method accurate to eight decimal places. Show all steps in solution. How many roots are there?

Answer #1

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

Use Newton's method to find all solutions of the equation
correct to eight decimal places. Start by drawing a graph to find
initial approximations. (Enter your answers as a comma-separated
list.) x x2 + 1 = 1 − x

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 find all solutions of the equation
correct to six decimal places. (Enter your answers as a
comma-separated list.)
x + 4
= x2 − x

For each equation, write a brief program to compute and print
eight steps of Newton's method for finding a positive root
(Preferably in Matlab or Python).
a. x=2sinx
b. x^3=sinx+7
c. sinx=1-x
d. x^5+x^2=1+7x^3 for x>=2

2.
Find a particular solution of x′′ + x = 8 cos^2 t using the method
of variation of parameters.

8. (a) Use Newton's method to find all solutions of the equation
correct to six decimal places. (Enter your answers as a
comma-separated list.) sqrt(x + 4) = x^2 − x 2.
(b) Use Newton's method to find the critical numbers of the
function: f(x) = x^6 − x^4 + 4x^3 − 3x, correct to six decimal
places. (Enter your answers as a comma-separated list.) x =

1. Find a particular solution of x′′ + x = 8 cos^2 t using the
method of undetermined coefficients.

Calculate two iterations of Newton's Method to approximate a zero
of the function using the given initial guess. (Round your answers
to four decimal places.)
f(x) = cos x, x1 = 0.8

Use Newton's method to find an approximate answer to the
question. Round to six decimal places. 2) Where is the first local
maximum of f(x) =3x sin x on the interval (0, Q)
located?

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