Question

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

Answer #1

**(a)**

**root = 0.754877666246693**

Matlab code:

format long;

x=5;

h = (x^5 + x -1) /(5*(x^4) + 1 );

i = 1;

while(abs(h) >= 0.00000001)

h = (x^5 + x -1) /(5*(x^4) + 1 );

x = x - h;

i=i+1;

end

x

**(b) root = -0.970898923504256**

**Matlab code:**

format long;

x=5;

h = (sin(x) - 6*x - 5) /(cos(x) -6 );

i = 1;

while(abs(h) >= 0.00000001)

h = (sin(x) - 6*x - 5) /(cos(x) -6 );

x = x - h;

i=i+1;

end

x

**c) root = 1.592142937058094**

**Matlab code:**

format long;

x=5;

h = (log(x) + x^2 - 3) /((1/x) + 2*x );

i = 1;

while(abs(h) >= 0.00000001)

h = (log(x) + x^2 - 3) /((1/x) + 2*x );

x = x - h;

i=i+1;

end

x

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

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