Question

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, x_{1} = 0.8

Answer #1

**Please comment if you have any doubt.**

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
n
xn
f(xn)
f '(xn)
f(xn)
f '(xn)
xn −
f(xn)
f '(xn)
1
2

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

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.)
45. f(x) = x5 −
5, x1 = 1.4
n
xn
f(xn)
f '(xn)
f(xn)
f '(xn)
xn −
f(xn)
f '(xn)
1
2
40. Find two positive numbers satisfying the given
requirements.
The product is 234 and the sum is a minimum.
smaller value=
larger value=
30.Determine the open intervals on which the graph is...

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 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) = x^5 + x −
7 Newton's method: x= Graphing utility: x =

46. 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) = 2 − x3
Newton's method:
Graphing utility:
x =
x =
48. Find the differential dy of the given function.
(Use "dx" for dx.)
y = x+1/3x-5
dy =
49.Find the differential dy of the given function.
y...

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

Complete four iterations of Newton’s Method for the function
f(x)=x^3+2x+1 using initial guess x1= -.5

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?

public static int newtonCount(double x, double err)
Determines the number of iterations of Newton's method required
to approximate the square root of x within the given bound.
Newton's method starts out by setting the initial approximate
answer to x. Then in each iteration, answer is
replaced by the quantity (answer + x / answer) / 2.0. The
process stops when the difference between x and (answer *
answer) is strictly less than the given bound err. The method
returns the...

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