Use Newton\'s method to approximate all the intersection points of the following

Question

Use Newton's method to approximate all the intersection points of the following pairs of curves. Some preliminary graphing or analysis may help in choosing good initial approximation. y = ln(x) and y = x^3 - 7 Now let x_0 = 5. Complete the table below using Newton's method. (Round to six decimal places as needed.) Continue applying Newton's method to the given values of x_0 as needed. The intersection points of the given curves occur at x (Use a comma to separate answers as needed. Round to six decimal places as needed.)

Explanation / Answer

here f(x) =x3-7-ln(x)

therefore f'(x) =3x2-1/x

hence from Newton' method;

xn =xn-1 -f(xn-1)/f'(xn-1)

from above

for intersection point is at x~1.972928

please revert for any clarifcation required

k xk 0 5 1 3.443976 2 2.519921 3 2.086897 4 1.979395 5 1.972951 6 1.972928 7 1.972928 8 1.972928 9 1.972928 10 1.972928

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