Question

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

Answer #1

**a) root =** 1.769292354238631

**Matlab code:**

format long;

x=5;

h = (x^3 -2*x - 2) /(3*(x^2) - 2);;

i = 1;

while(abs(h) >= 0.00000001)

h = (x^3 -2*x - 2) /(3*(x^2) - 2);

x = x - h;

i=i+1;

end

x

**b) root = 1.672821698628906**

**Matlab code:**

format long;

x=5;

h = (exp(x) + x - 7) /(exp(x) + 1 );

i = 1;

while(abs(h) >= 0.00000001)

h = (exp(x) + x - 7) /(exp(x) + 1 );

x = x - h;

i=i+1;

end

x

**c) root = 1.129980498650833**

**Matlab code:**

format long;

x=5;

h = (exp(x) + sin(x) - 4) /(exp(x) + cos(x) );

i = 1;

while(abs(h) >= 0.00000001)

h = (exp(x) + sin(x) - 4) /(exp(x) + cos(x));

x = x - h;

i=i+1;

end

x

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 all solutions of the equation
correct to eight decimal places.
7? −?^2 sin ? = ?^2 − ? + 1

Use Newton's method to find all the roots of the equation
correct to eight decimal places. Start by drawing a graph to find
initial approximations.
3 sin(x2) = 2x

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 the Bisection Method to locate all solutions of the
following equations. Sketch the
function by using Matlab’s plot command and identify three
intervals of length one that
contain a root. Then find the roots to six correct decimal places.
(a) 2x3 − 6x − 1 = 0
(b) ex−2 + x3 − x = 0 (c) 1 + 5x − 6x3 − e2x = 0
**MUST BE DONE IN MATLAB AND NEEDS CODE

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

The given equation has a root in the indicated interval.In
MatLab, use the Bisection method to generate the first four
midpoints and intervals (besides the original interval given)
containing the root.
equation: e^x - 2x= 2,[0,2]

Use Newton's method to find all solutions of the equation
correct to eight decimal places. Start by drawing a graph to find
initial approximations. (Enter your answers as a comma-separated
list.) x x2 + 1 = 1 − x

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

: 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.

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