Question

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

Answer #1

Newton's method to solve f(x)=0

Let f(x) is continuous function on [a,b]

Then solution in [a,b] is given by

Here

And it's derivative is

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

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.)...

A graphing calculator is recommended. 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.) -2x^7-4x^4+9x^3+2=0

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

Approximate the zero for f(x) = (x^3)+(4x^2)-3x-8 using newton's
method
Use x1 = -6
A)Find x2,x3,x4,x5,x6
B)Based on the result, you estimate the zero for the function to
be......?
C)Explain why choosing x1 = -3 would have been a bad idea?
D) Are there any other bad ideas that someone could have chosen
for x1?

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 =

Calculate two iterations of Newton's Method to approximate a
zero of the function using the given initial guess. (Round your
answers to three decimal places.) f(x) = x3 − 3, x1 = 1.6

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?

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

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