Question

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

Answer #1

Here

Let

Iteration -1 :

Iteration -2 :

Iteration - 3:

Iteration - 4:

17. I am using Newton’s method to ﬁnd the negative root of f(x)
= 3−x2.
(a) What would be a good guess for x1? Draw the line
tangent to f(x) at your x1 and explain why using
Newton’s method would lead to the negative root of the
function.
(b) What would be a bad guess for x1? Draw the line
tangent to f(x) at your x1 and explain why using
Newton’s method would not lead to the negative root of...

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 approximate a critical
number of the function ?(?)=(1/3)?^3−2?+6.
f(x)=1/3x^3−2x+6 near the point ?=1x=1. Find the next two
approximations, ?2 and ?3 using ?1=1. x1=1 as the initial
approximation.

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

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.)...

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

2. Perform 2 iterations of Newton’s method on
f(x,y)=x^4+4x^2*y+4y^2+2x+2y starting at(1,1).

2. (a) For the equation e^x = 3 - 2 x , find a function, f(x),
whose x-intercept is the solution of the equation (i.e. a function
suitable to use in Newton’s Method), and use it to set up xn+1 for
Newton’s Method.
(b) Use Newton's method to find x3 , x4 and x5 using the initial
guess x1 = 0 . How many digits of accuracy are you certain of from
these results?
(c) Use x1+ ln 2 and show...

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...

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