Question 3. [15 points] On most computers, the computation of \\/a is based on Newton's method for finding a root of f(a) = ?a. Here, we assume a 0. We want to use Newton's method to solve this root-finding problem. L. What is the iteration formula of Newton's method for the above f(x)? 2. Note that 2* = ,/a is a root of f(x). Derive the error and relative error formulas: 1 va n41 = -~(Va _ Ln)? 220 Rel(tn44) = -M Rel(en) where Rel(x,,) = var tn is the relative error. (Hint: use the error formula of Newton's v f" (cn) 2f'(2n) method for finding a root * of function f: 2* r,41 = (x* In)" ( ), where Cn is a number between x* and :,,.) 3. For 29 near 4/a, the last formula becomes 1 2 Rel(ty41) 5 Rel(2n) Wn =O0,1.... Assume Rel(ao) = 0.1, use this formula to estimate the relative error in 2, :r2, 3