Question

Use
Newton’s Method to approximate the real solutions of x^5 + x −1 = 0
to five decimal places.

Answer #1

Each equation has one real root. Use Newton’s Method to
approximate the root to eight correct decimal places. (a) x5 + x =
1 (b) sin x = 6x + 5 (c) ln x + x2 = 3
**MUST BE DONE IN MATLABE AND SHOW CODE

Use Newton’s method to find solutions accurate to within 10−4
for x − 0.8 − 0.2 sin x = 0, x in[0, π/2]. (Choose ?0=π/4).

Use Newton’s method to find all solutions of the equation
correct to six decimal places: ?^2 − ? = √? + 1

: Consider f(x) = 3 sin(x2) − x.
1. Use Newton’s Method and initial value x0 = −2 to approximate
a negative root of f(x) up to 4 decimal places.
2. Consider the region bounded by f(x) and the x-axis over the
the interval [r, 0] where r is the answer in the previous part.
Find the volume of the solid obtain by rotating the region about
the y-axis. Round to 4 decimal places.

Use Newton’s method to find all solutions of the equation
correct to eight decimal places.
7? −?^2 sin ? = ?^2 − ? + 1

Each equation has one root. Use Newton’s Method to approximate
the root to eight correct
decimal places. (a) x3 = 2x + 2 (b) ex + x = 7 (c) ex + sin x =
4
**MUST BE DONE IN MATLAB AND NEED CODE

The function e^x −100x^2 =0 has three true solutions.Use
Newton’s method to locate the solutions with tolerance
10^(−10).

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 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.

Suppose that Newton’s method is applied to find the solution p
= 0 of the equation
e^x −1−x− (1/2)x^2 = 0. It is known that, starting with any p0
> 0, the sequence {pn} produced by the Newton’s method is
monotonically decreasing (i.e., p0 >p1 >p2 >···)and
converges to 0.
Prove that {pn} converges to 0 linearly with rate 2/3. (hint:
You need to have the patience to use L’Hospital rule repeatedly. )
Please do the proof.

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