Let a > 0 be given and suppose we want to approximate √a using Newton’s method. 

a. Explain why the square root problem is equivalent to finding the positive root of f(x) = x² - a.

b. Show that Newton’s method applied to this function takes the form (sometimes called the Babylonian method).

c. How would you choose initial approximations to approximate √13 and √73?

d. Approximate √13 and √73 with at least 10 significant digits.

Transcribed Image Text:

for n = 0, 1, 2, . . .. Хп. Хл+1 Xn