Question

Use Newton's method to approximate a root of

f(x) = 10x^{2} + 34x -14 if the initial approximation is
x_{o} = 1

x_{1} =

x_{2} =

x_{3} =

x_{4} =

Answer #1

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
.

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?

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 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 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

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

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

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 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) = -x3 - cos x and p0 = -1 . Use
Newton's method to find p1 and the Secant method to find
p2

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