Show Newton's method for the square root of a is the average of guess and a/guess....

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Show Newton's method for the square root of a is the average of guess and a/guess. That is, show that Newton's Method for finding the positive square root of a positive Note that: if our current guess, Xn, IS number, a, can be given by x+1 Xn+1 X₂ too low then a/x, is too high and vice versa. So taking the average of the two should be an improvement. Show that Newton's method for x² - a=0 can be written as 1 == 2 1 = x₂ +- 2 a x₁₂ + = X₂ a Show Newton's method for the square root of a is the average of guess and a/guess. That is, show that Newton's Method for finding the positive square root of a positive Note that: if our current guess, Xn, IS number, a, can be given by x+1 Xn+1 X₂ too low then a/x, is too high and vice versa. So taking the average of the two should be an improvement. Show that Newton's method for x² - a=0 can be written as 1 == 2 1 = x₂ +- 2 a x₁₂ + = X₂ a

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According to Newtons formula fxn fx... View the full answer