Your task is to design algorithms to solve the following problems. For full credit, your algorithm must run in logarithmic time. Root-finding Given a number n Greaterthanorequalto 1 and a (user-specified) error tolerance e, you want to approximate the squareroot of n to within error tolerance e. Specifically, you want to return an x Squareroot n that satisfies |x^2 - n| lessthanorequalto e. For example, to compute the squareroot of n = 2 with e = 0.01, an acceptable answer would be x = 1.414, because 1.414^2 = 1.999396. Note that x = 1.415 is also acceptable, as 1.415^2 = 2.002225, but you only need to return a single answer. Assume that you can't perform any arithmetic functions other than addition, subtraction, multiplication, and division. Write for an efficient algorithm to solve this problem. Briefly justify a good asymptotic bound on the runtime of your algorithm in terms of n (i.e., give a runtime in terms of n assuming a fixed value of e). BONUS: Provide an asymptotic bound on the runtime of your algorithm in terms of e, for a fixed value of n. Prove your result