Question

Use Newton's method to find the number arcsin(1/3) rounded to 14 digits after the decimal point by solving numerically the equation sin(x)=1/3 on the interval [0,pi/6].

1) Determine f(a) and f(b).

2) Find analytically f', f'' and check if f '' is continuous on the chosen interval [a,b].

3) Determine the sign of f' and f '' on [a,b] using their plots.

4) Determine using the plot the upper bound C and the lower bound c for |f'(x)|.

5) Calculate the function g(x).

6) Determine an upper bound N for |f ''(x)| on [0.4,1] using its plot on [0.39,1].

7) Determine the initial point x_0.

8) Run the iterations of the Newton's method until the error condition is satisfied and roundoff the answer.

Just part 8 please. Please show all steps and calculations. Thank you

Answer #1

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.)...

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 =

Find n for which the nth iteration by the fixed point method is
guaranteed to approximate the root of f(x) = x − cos x on [0, π/3]
with an accuracy within 10−8 using x0 = π/4
Answer: n = 127 iterations or n = 125 iterations.
Please show work to get to answer

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...

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...

Newton's method: For a function ?(?)=ln?+?2−3f(x)=lnx+x2−3
a. Find the root of function ?(?)f(x) starting with
?0=1.0x0=1.0.
b. Compute the ratio |??−?|/|??−1−?|2|xn−r|/|xn−1−r|2, for
iterations 2, 3, 4 given ?=1.592142937058094r=1.592142937058094.
Show that this ratio's value approaches
|?″(?)/2?′(?)||f″(x)/2f′(x)| (i.e., the iteration converges
quadratically). In error computation, keep as many digits as you
can.

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?

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.

Let
f(x)=sin(x)+x^3-2. Use the secant method to find a root of f(x)
using initial guesses x0=1 and x1=4. Continue until two consecutive
x values agree in the first 2 decimal places.

Question 1
Amanda, a local supermarket owner, has decided to use a more
analytical approach to improve her store's customer service. Her
goal is to maintain the ratio of people working in the store over
the number of customers around 1.5. What this means is, for
example, for every two customers at any point in time there would
be three people working at the store.
In order for her to achieve this ratio, she wants to re-evaluate
her knowledge about...

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