(1) We wish to estimate the unique real root of f (:r) = 1:5 :c 1 by using Newton's method. (a) Determine the formula for 15,1\" in terms of :13\". (b) Using the initial estimate m0 = 1.25, determine the estimate m5. You may use a calculator or computer and should write out at least nine decimal places for each of 1:1,:1:2, 1:3, $4,415. (2) ((1) sin :1: + cos a: (3) Verify that a: arcsinrz: + v1 3:2 is an antiderivative of arcsin 1:. (4) Suppose that an object is subject to a sinusoidal driving force that produces an acceleration Asin(wt + (p), where A,w, 99 are constants and w 75 0. (a) Determine the generic formula for the velocity as a function of time. (b) Determine the generic formula for the position as a function of time. (c) Determine the specic formula for the position as a function of time given that the position and velocity at time t = 0 are both 0